Conversion of units 1

Conversion of unitsConversion of units refers to conversion factors between different units of measurement for the same quantity

Techniques

ProcessThe process of conversion depends on the specific situation and the intended purpose This may be governed byregulation contract Technical specifications or other published standards Engineering judgment may include suchfactors asbull The precision and accuracy of measurement and the associated uncertainty of measurementbull The statistical confidence interval or tolerance interval of the initial measurementbull The number of significant figures of the measurementbull The intended use of the measurement including the engineering tolerancesSome conversions from one system of units to another need to be exact without increasing or decreasing theprecision of the first measurement This is sometimes called soft conversion It does not involve changing thephysical configuration of the item being measuredBy contrast a hard conversion or an adaptive conversion may not be exactly equivalent It changes the measurementto convenient and workable numbers and units in the new system It sometimes involves a slightly differentconfiguration or size substitution of the item

Multiplication FactorsConversion between units in the metric system can be discerned by their prefixes (for example 1 kilogram =1000 grams 1 milligram = 0001 grams) and are thus not listed in this article Exceptions are made if the unit iscommonly known by another name (for example 1 micron = 10minus6 metre)

Table OrderingWithin each table the units are listed alphabetically and the SI units (base or derived) are highlighted

Tables of conversion factorsThis article gives lists of conversion factors for each of a number of physical quantities which are listed in the indexFor each physical quantity a number of different units (some only of historical interest) are shown and expressed interms of the corresponding SI unit

Conversion of units 2

Legend

Symbol Definition

equiv exactly equal to

asymp approximately equal to

digits indicates that digits repeat infinitely (eg 8294369 corresponds to 8294369369369369hellip)

(H) of chiefly historical interest

Length

Length

Name of unit Symbol Definition Relation to SI units

aringngstroumlm Aring equiv 1 times 10minus10 m equiv 01 nm

astronomical unit AU asymp Distance from Earth to Sun asymp 149597871464 m [1]

barleycorn (H) = ⅓ in (see note above about rounding) asymp 846times10minus3 m

bohr atomic unit oflength

a0 equiv Bohr radius of hydrogen asymp 52917720859 times 10minus11 plusmn 36 times 10minus20 m[2]

cable length (Imperial) equiv 608 ft asymp 1853184 m

cable length(International)

equiv 110 nmi equiv 1852 m

cable length (US) equiv 720 ft = 219456 m

chain (GuntersSurveyors)

ch equiv 66 ft(US) equiv 4 rods [3] asymp 2011684 m

cubit (H) equiv Distance from fingers to elbow asymp 18 in asymp 05 m

ell (H) ell equiv 45 in [4] (In England usually) = 1143 m

fathom fm equiv 6 ft [4] = 18288 m

fermi fm equiv 1 times 10minus15 m[4] equiv 1 times 10minus15 m

finger equiv 78 in = 0022225 m

finger (cloth) equiv 4frac12 in = 01143 m

foot (Benoicirct) (H) ft (Ben) asymp 0304799735 m

foot (Clarkes Cape) (H) ft (Cla) asymp 03047972654 m

foot (Indian) (H) ft Ind asymp 0304799514 m

foot (International) ft equiv 13 yd equiv 03048 m equiv 12 inches equiv 03048 m

foot (Sears) (H) ft (Sear) asymp 030479947 m

foot (US Survey) ft (US) equiv 1200frasl3937 m [5] asymp 0304800610 m

french charriere F equiv 1frasl3 mm = 03 times10minus3 m

furlong fur equiv 10 chains = 660 ft = 220 yd [4] = 201168 m

hand equiv 4 in [4] equiv 01016 m

Conversion of units 3

inch (International) in equiv 136 yd equiv 112 ft equiv 00254 m

league (land) lea equiv 3 US Statute miles [3] = 4828032 m

light-day equiv 24 light-hours equiv 259020683712 times 1013 m

light-hour equiv 60 light-minutes equiv 10792528488 times 1012 m

light-minute equiv 60 light-seconds equiv 1798754748 times 1010 m

light-second equiv Distance light travels in one second in vacuum equiv 299792458 m

light-year ly equiv Distance light travels in vacuum in 36525 days [6] = 94607304725810 times 1015 m

line ln equiv 112 in [7] = 0002116 m

link (Gunters Surveyors) lnk equiv 1100 ch [4] equiv 066 ft equiv 792in = 0201168 m

link (RamsdensEngineers)

lnk equiv 1 ft [4] = 03048 m

metre (SI base unit) m equiv Distance light travels in 1frasl299792458 of a second invacuum[8]

asymp 1frasl10000000 of the distance from equator to pole

equiv 1 m

mickey equiv 1frasl200 in = 127 times 10minus4 m

micron micro equiv 1 times 10minus6 m

mil thou mil equiv 1 times 10minus3 in equiv 254 times 10minus5 m

mil (Sweden and Norway) mil equiv 10 km = 10000 m

mile (geographical) (H) equiv 6082 ft = 18537936 m

mile (international) mi equiv 80 chains equiv 5280 ft equiv 1760 yd equiv 1609344 m

mile (tactical or data) equiv 6000 ft equiv 18288 m

mile (telegraph) (H) mi equiv 6087 ft = 18553176 m

mile (US Survey) mi equiv 5280 US Survey feet equiv (5280 times 1200frasl3937) m asymp 1609347219 m

nail (cloth) equiv 2frac14 in [4] = 0057 15 m

nanometer nm equiv 1 times 10minus9 m equiv 1 times 10minus9 m

nautical league NL nl equiv 3 nmi [4] = 5556 m

nautical mile (Admiralty) NM (Adm) nmi(Adm)

= 6080 ft = 1853184 m

nautical mile(international)

NM nmi equiv 1852 m [9] equiv 1852 m

nautical mile (US pre1954)

equiv 1853248 m equiv 1853248 m

pace equiv 25 ft [4] = 0762 m

palm equiv 3 in [4] = 00762 m

parsec pc Distance of star with parallax shift of one arc secondfrom a base of one astronomical unit

asymp 3085 677 82times1016 plusmn 6times106 m [10]

pica equiv 12 points Dependent on point measures

Conversion of units 4

point (American English)[11] [12]

pt equiv 172272 in asymp 0000 351 450 m

point (Didot European)[12] [13]

pt equiv 112 times 172 of pied du roiAfter 1878equiv 5133 cm

asymp 0000 375 97 mAfter 1878asymp 0000 375 939 85 m

point (PostScript) [11] pt equiv 172 in = 0000 352 7 m

point (TeX) [11] pt equiv 17227 in = 0000 351 4598 m

quarter equiv frac14 yd = 02286 m

rod pole perch (H) rd equiv 16frac12 ft = 50292 m

rope (H) rope equiv 20 ft [4] = 6096 m

span (H) equiv 9 in [4] = 02286 m

spat [14] equiv 1times1012 m

stick (H) equiv 2 in = 00508 m

stigma bicron(picometre)

pm equiv 1times10minus12 m

twip twp equiv 11440 in = 17638times10minus5 m

x unit siegbahn xu asymp 10021times10minus13 m [4]

yard (International) yd equiv 09144 m [5] equiv 3 ft equiv 36 in equiv 09144 m

Area

Area

Name of unit Symbol Definition Relation to SI units

acre (international) ac equiv 1 ch times 10 ch = 4840 sq yd equiv 4 046856 4224 m2

acre (U S survey) ac equiv 10 sq ch = 4840 sq yd also 43560 sq ft asymp 4 046873 m2 [15]

are a equiv 100 m2 = 100 m2

barn b equiv 10minus28 m2 = 10minus28 m2

barony equiv 4000 ac asymp 1618 742times107 m2

board bd equiv 1 in times 1 ft = 7741 92times10minus3 m2

boiler horsepower equivalent direct radiation bhp EDR equiv (1 ft2) (1 bhp) (240 BTUITh) asymp 12958 174 m2

circular inch circ in equiv π4 sq in asymp 5067 075times10minus4 m2

circular mil circular thou circ mil equiv π4 mil2 asymp 5067 075times10minus10 m2

cord equiv 192 bd = 1486 448 64 m2

dunam equiv 1 000 m2 = 1 000 m2

guntha equiv 121 sq yd asymp 10117 m2

hectare ha equiv 10 000 m2 equiv 10 000 m2

Conversion of units 5

hide asymp 120 ac (variable) asymp 5times105 m2

rood ro equiv frac14 ac = 1 011714 1056 m2

section equiv 1 mi times 1 mi = 2589 988 110 336times106 m2

shed equiv 10minus52 m2 = 10minus52 m2

square (roofing) equiv 10 ft times 10 ft = 9290 304 m2

square chain (international) sq ch equiv 66 ft times 66 ft = 110 ac equiv 404685 642 24 m2

square chain (US Survey) sq ch equiv 66 ft(US) times 66 ft(US) = 110 ac asymp 404687 3 m2

square foot sq ft equiv 1 ft times 1 ft equiv 9290 304times10minus2 m2

square foot (US Survey) sq ft equiv 1 ft (US) times 1 ft (US) asymp 9290 341 161 327 49times10minus2 m2

square inch sq in equiv 1 in times 1 in equiv 64516times10minus4 m2

square kilometre km2 equiv 1 km times 1 km = 106 m2

square link (Gunters)(International) sq lnk equiv 1 lnk times 1 lnk equiv 066 ft times 066 ft = 4046 856 4224times10minus2 m2

square link (Gunters)(US Survey) sq lnk equiv 1 lnk times 1 lnk equiv 066 ft(US) times 066 ft(US) asymp 4046 872times10minus2 m2

square link (Ramsdens) sq lnk equiv 1 lnk times 1 lnk equiv 1 ft times 1 ft = 009290304 m2

square metre (SI unit) m2 equiv 1 m times 1 m = 1 m2

square mil square thou sq mil equiv 1 mil times 1 mil = 64516times10minus10 m2

square mile sq mi equiv 1 mi times 1 mi = 2589 988 110 336times106 m2

square mile (US Survey) sq mi equiv 1 mi (US) times 1 mi (US) asymp 2589 998 47times106 m2

square rodpoleperch sq rd equiv 1 rd times 1 rd = 25292 852 64 m2

square yard (International) sq yd equiv 1 yd times 1 yd equiv 0836 127 36 m2

stremma equiv 1 000 m2 = 1 000 m2

township equiv 36 sq mi (US) asymp 9323 994times107 m2

yardland asymp 30 ac asymp 12times105 m2

Volume

Conversion of units 6

Volume

Name of unit Symbol Definition Relation to SI units

acre-foot ac ft equiv 1 ac x 1 ft = 43 560 ft3 = 1 233481 837 547 52 m3

acre-inch equiv 1 ac times 1 in = 102790 153 128 96 m3

barrel (Imperial) bl (Imp) equiv 36 gal (Imp) = 0163 659 24 m3

barrel (petroleum) bl bbl equiv 42 gal (US) = 0158 987 294 928 m3

barrel (US dry) bl (US) equiv 105 qt (US) = 10532 bu (US lvl) = 0115 628 198 985 075 m3

barrel (US fluid) fl bl (US) equiv 31frac12 gal (US) = 0119 240 471 196 m3

board-foot fbm equiv 144 cu in equiv 2359 737 216times10minus3 m3

bucket (Imperial) bkt equiv 4 gal (Imp) = 0018 184 36 m3

bushel (Imperial) bu (Imp) equiv 8 gal (Imp) = 0036 368 72 m3

bushel (US dry heaped) bu (US) equiv 1 frac14 bu (US lvl) = 0044 048 837 7086 m3

bushel (US dry level) bu (US lvl) equiv 2 15042 cu in = 0035 239 070 166 88 m3

butt pipe equiv 126 gal (wine) = 0476 961 884 784 m3

coomb equiv 4 bu (Imp) = 0145 474 88 m3

cord (firewood) equiv 8 ft times 4 ft times 4 ft = 3624 556 363 776 m3

cord-foot equiv 16 cu ft = 0453 069 545 472 m3

cubic fathom cu fm equiv 1 fm times 1 fm times 1 fm = 6116 438 863 872 m3

cubic foot cu ft equiv 1 ft times 1 ft times 1 ft equiv 0028 316 846 592 m3

cubic inch cu in equiv 1 in times 1 in times 1 in equiv 16387 064times10minus6 m3

cubic metre (SI unit) m3 equiv 1 m times 1 m times 1 m equiv 1 m3

cubic mile cu mi equiv 1 mi times 1 mi times 1 mi equiv 4 168 181 825440 579 584 m3

cubic yard cu yd equiv 27 cu ft equiv 0764 554 857 984 m3

cup (breakfast) equiv 10 fl oz (Imp) = 284130 625times10minus6 m3

cup (Canadian) c (CA) equiv 8 fl oz (Imp) = 2273045times10minus6 m3

cup (metric) c equiv 2500times10minus6 m3 = 2500times10minus6 m3

cup (US customary) c (US) equiv 8 US fl oz equiv 116 gal (US) = 236588 2365times10minus6 m3

cup (US food nutrition labeling) c (US) equiv 240 mL[16] = 24 times 10minus4 m3

dash (Imperial) equiv 1384 gi (Imp) = frac12 pinch (Imp) = 369961 751 302 08 3times10minus9 m3

dash (US) equiv 196 US fl oz = frac12 US pinch = 308057 599 609 375times10minus9 m3

dessertspoon (Imperial) equiv 112 gi (Imp) = 11838 776 0416times10minus6 m3

drop (Imperial) gtt equiv 1288 fl oz (Imp) = 98656 467 013 8times10minus9 m3

Conversion of units 7

drop (Imperial) (alt) gtt equiv 11 824 gi (Imp) asymp 77886 684times10minus9 m3

drop (medical) equiv 112 ml = 8303times10minus9 m3

drop (metric) equiv 120 mL = 500times10minus9 m3

drop (US) gtt equiv 1360 US fl oz = 82148 693 22916times10minus9 m3

drop (US) (alt) gtt equiv 1456 US fl oz asymp 64854 231times10minus9 m3

fifth equiv 15 US gal = 757082 3568times10minus6 m3

firkin equiv 9 gal (US) = 0034 068 706 056 m3

fluid drachm (Imperial) fl dr equiv ⅛ fl oz (Imp) = 3551 632 8125times10minus6 m3

fluid dram (US) US fluidram fl dr equiv ⅛ US fl oz = 3696 691 195 3125times10minus6 m3

fluid scruple (Imperial) fl s equiv 124 fl oz (Imp) = 1183 877 60416times10minus6 m3

gallon (beer) beer gal equiv 282 cu in = 4621 152 048times10minus3 m3

gallon (Imperial) gal (Imp) equiv 4546 09 L equiv 4546 09times10minus3 m3

gallon (US dry) gal (US) equiv ⅛ bu (US lvl) = 4404 883 770 86times10minus3 m3

gallon (US fluid Wine) gal (US) equiv 231 cu in equiv 3785 411 784times10minus3 m3

gill (Imperial) Noggin gi (Imp) nog equiv 5 fl oz (Imp) = 142065 3125times10minus6 m3

gill (US) gi (US) equiv 4 US fl oz = 118294 118 25times10minus6 m3

hogshead (Imperial) hhd (Imp) equiv 2 bl (Imp) = 0327 318 48 m3

hogshead (US) hhd (US) equiv 2 fl bl (US) = 0238 480 942 392 m3

jigger (bartending) equiv 1frac12 US fl oz asymp 4436times10minus6 m3

kilderkin equiv 18 gal (Imp) = 0081 829 62 m3

lambda λ equiv 1 mm3 = 1times10minus9 m3

last equiv 80 bu (Imp) = 2909 4976 m3

litre L equiv 1 dm3 [17] equiv 0001 m3

load equiv 50 cu ft = 1415 842 3296 m3

minim (Imperial) min equiv 1480 fl oz (Imp) = 160 fl dr (Imp) = 59193 880 208 3times10minus9 m3

minim (US) min equiv 1480 US fl oz = 160 US fl dr = 61611 519 921 875times10minus9 m3

ounce (fluid Imperial) fl oz (Imp) equiv 1160 gal (Imp) equiv 28413 0625times10minus6 m3

ounce (fluid US customary) US fl oz equiv 1128 gal (US) equiv 29573 529 5625times10minus6 m3

ounce (fluid US food nutrition labeling) US fl oz equiv 30 mL[16] equiv 3 times 10minus5 m3

peck (Imperial) pk equiv 2 gal (Imp) = 9092 18times10minus3 m3

peck (US dry) pk equiv frac14 US lvl bu = 8809 767 541 72times10minus3 m3

perch per equiv 16frac12 ft times 1frac12 ft times 1 ft = 0700 841 953 152 m3

Conversion of units 8

pinch (Imperial) equiv 1192 gi (Imp) = ⅛ tsp (Imp) = 739923 502 60416times10minus9 m3

pinch (US) equiv 148 US fl oz = ⅛ US tsp = 616115 199 218 75times10minus9 m3

pint (Imperial) pt (Imp) equiv ⅛ gal (Imp) = 568261 25times10minus6 m3

pint (US dry) pt (US dry) equiv 164 bu (US lvl) equiv ⅛ gal (US dry) = 550610 471 3575times10minus6 m3

pint (US fluid) pt (US fl) equiv ⅛ gal (US) = 473176 473times10minus6 m3

pony equiv 34 US fl oz = 22180 147 171 875times10minus6 m3

pottle quartern equiv frac12 gal (Imp) = 80 fl oz (Imp) = 2273 045times10minus3 m3

quart (Imperial) qt (Imp) equiv frac14 gal (Imp) = 1136 5225times10minus3 m3

quart (US dry) qt (US) equiv 132 bu (US lvl) = frac14 gal (US dry) = 1101 220 942 715times10minus3 m3

quart (US fluid) qt (US) equiv frac14 gal (US fl) = 946352 946times10minus6 m3

quarter pail equiv 8 bu (Imp) = 0290 949 76 m3

register ton equiv 100 cu ft = 2831 684 6592 m3

sack (Imperial) bag equiv 3 bu (Imp) = 0109 106 16 m3

sack (US) equiv 3 bu (US lvl) = 0105 717 210 500 64 m3

seam equiv 8 bu (US lvl) = 0281 912 561 335 04 m3

shot equiv 1 US fl oz asymp 2957times10minus6 m3

strike (Imperial) equiv 2 bu (Imp) = 0072 737 44 m3

strike (US) equiv 2 bu (US lvl) = 0070 478 140 333 76 m3

tablespoon (Australian metric) equiv 200times10minus6 m3

tablespoon (Canadian) tbsp equiv frac12 fl oz (Imp) = 14206 531 25times10minus6 m3

tablespoon (Imperial) tbsp equiv 58 fl oz (Imp) = 17758 164 0625times10minus6 m3

tablespoon (metric) equiv 150times10minus6 m3

tablespoon (US customary) tbsp equiv frac12 US fl oz = 14786 764 7825times10minus6 m3

tablespoon (US food nutrition labeling) tbsp equiv 15 mL[16] = 15 times 10minus5 m3

teaspoon (Canadian) tsp equiv 16 fl oz (Imp) = 4735 510 416times10minus6 m3

teaspoon (Imperial) tsp equiv 124 gi (Imp) = 5919 388 02083times10minus6 m3

teaspoon (metric) equiv 50times10minus6 m3 = 50times10minus6 m3

teaspoon (US customary) tsp equiv 16 US fl oz = 4928 921 595times10minus6 m3

teaspoon (US food nutrition labeling) tsp equiv 5 mL[16] = 5 times 10minus6 m3

timber foot equiv 1 cu ft = 0028 316 846 592 m3

ton (displacement) equiv 35 cu ft = 0991 089 630 72 m3

ton (freight) equiv 40 cu ft = 1132 673 863 68 m3

Conversion of units 9

ton (water) equiv 28 bu (Imp) = 1018 324 16 m3

tun equiv 252 gal (wine) = 0953 923 769 568 m3

wey (US) equiv 40 bu (US lvl) = 1409 562 806 6752 m3

Plane angle

Plane angle

Name of unit Symbol Definition Relation to SIunits

angular mil micro equiv 2π6400 rad asymp 0981 748times10minus3

rad

arcminute moa equiv 1deg60 asymp 0290 888times10minus3

rad

arcsecond equiv 1deg3600 asymp 4848 137times10minus6

rad

centesimal minuteof arc

equiv 1 grad100 asymp 0157 080times10minus3

rad

centesimal secondof arc

equiv 1 grad(10 000) asymp 1570 796times10minus6

rad

degree (of arc) deg equiv 1360 of a revolution equiv π180 rad asymp 17453293times10minus3 rad

grad gradian gon grad equiv 1400 of a revolution equiv 2π400 rad equiv 09deg asymp 15707963times10minus3 rad

octant equiv 45deg asymp 0785 398 rad

quadrant equiv 90deg asymp 1570 796 rad

radian (SI unit) rad The angle subtended at the center of a circle by an arc whose length is equal to the circlesradius One full revolution encompasses 2π radians

= 1 rad

sextant equiv 60deg asymp 1047 198 rad

sign equiv 30deg asymp 0523 599 rad

Conversion of units 10

Solid angle

Solid angle

Name of unit Symbol Definition Relation to SIunits

steradian (SIunit)

sr The solid angle subtended at the center of a sphere of radius r by a portion of the surface of the spherehaving an area r2 A sphere encompasses 4π sr[14]

= 1 sr

MassNotesbull See Weight for detail of massweight distinction and conversionbull In this table the unit gee is used to denote standard gravity in order to avoid confusion with the g symbol for

gramsbull In physics the pound of mass is sometimes written lbm to distinguish it from the pound-force (lbf) It should not

be read as the mongrel unit pound metre

Mass

Name of unit Symbol Definition Relation to SI units

atomic mass unit unified u AMU asymp 1660 538 73times10minus27 plusmn 13times10minus36 kg

atomic unit of mass electron restmass

me asymp 9109 382 15times10minus31 plusmn 45times10minus39 kg[18]

bag (coffee) equiv 60 kg = 60 kg

bag (Portland cement) equiv 94 lb av = 42637 682 78 kg

barge equiv 22frac12 sh tn = 20 411656 65 kg

carat kt equiv 3 16 gr asymp 205196 548 333 mg

carat (metric) ct equiv 200 mg = 200 mg

clove equiv 8 lb av = 3628 738 96 kg

crith asymp 899349 mg

dalton Da asymp 1660 902 10times10minus27 plusmn 13times10minus36 kg

dram (apothecary troy) dr t equiv 60 gr = 3887 9346 g

dram (avoirdupois) dr av equiv 27 1132 gr = 1771 845 195 3125 g

electronvolt eV equiv 1 eV (energy unit) c2 = 17826times10minus36 kg

gamma γ equiv 1 μg = 1 μg

grain gr equiv 17000 lb av equiv 64798 91 mg

grave G grave was the original name of the kilogram equiv 1 kg

hundredweight (long) long cwt orcwt

equiv 112 lb av = 50802 345 44 kg

hundredweight (short) cental sh cwt equiv 100 lb av = 45359 237 kg

hyl (CGS unit) equiv 1 gee times 1 g times 1 s2m = 9806 65 g

hyl (MKS unit) equiv 1 gee times 1 kg times 1 s2m = 9806 65 kg

Conversion of units 11

kilogram kg equiv mass of the prototype near Paris (asymp mass of 1L ofwater)

equiv 1 kg (SI base unit)[8]

kip kip equiv 1000 lb av = 453592 37 kg

mark equiv 8 oz t = 248827 8144 g

mite equiv 120 gr = 3239 9455 mg

mite (metric) equiv 120 g = 50 mg

ounce (apothecary troy) oz t equiv 112 lb t = 31103 4768 g

ounce (avoirdupois) oz av equiv 116 lb = 28349 523 125 g

ounce (US food nutrition labeling) oz equiv 28 g[16] = 28 g

pennyweight dwt pwt equiv 120 oz t = 1555 173 84 g

point equiv 1100 ct = 2 mg

pound (avoirdupois) lb av equiv 0453 592 37 kg = 7000 grains equiv 0453 592 37 kg

pound (metric) equiv 500 g = 500 g

pound (troy) lb t equiv 5 760 grains = 0373 241 7216 kg

quarter (Imperial) equiv 14 long cwt = 2 st = 28 lb av = 12700 586 36 kg

quarter (informal) equiv frac14 short tn = 226796 185 kg

quarter long (informal) equiv frac14 long tn = 254011 7272 kg

quintal (metric) q equiv 100 kg = 100 kg

scruple (apothecary) s ap equiv 20 gr = 1295 9782 g

sheet equiv 1700 lb av = 6479891 mg

slug geepound slug equiv 1 gee times 1 lb av times 1 s2ft asymp 14593 903 kg

stone st equiv 14 lb av = 6350 293 18 kg

ton assay (long) AT equiv 1 mg times 1 long tn divide 1 oz t asymp 32666 667 g

ton assay (short) AT equiv 1 mg times 1 sh tn divide 1 oz t asymp 29166 667 g

ton long long tn or ton equiv 2 240 lb = 1 016046 9088 kg

ton short sh tn equiv 2 000 lb = 907184 74 kg

tonne (mts unit) t equiv 1 000 kg = 1 000 kg

wey equiv 252 lb = 18 st = 114305 277 24 kg (variants exist)

Zentner Ztr Definitions vary see [19] and[14]

Density

Conversion of units 12

Density

Name of unit Symbol Definition Relation to SI units

gram per millilitre gmL equiv gmL = 1000 kgm3

kilogram per cubic metre (SI unit) kgm3 equiv kgm3 = 1 kgm3

kilogram per litre kgL equiv kgL = 1000 kgm3

ounce (avoirdupois) per cubic foot ozft3 equiv ozft3 asymp 1001153961 kgm3

ounce (avoirdupois) per cubic inch ozin3 equiv ozin3 asymp 1729994044 times 103 kgm3

ounce (avoirdupois) per gallon (Imperial) ozgal equiv ozgal asymp 6236023291 kgm3

ounce (avoirdupois) per gallon (US fluid) ozgal equiv ozgal asymp 7489151707 kgm3

pound (avoirdupois) per cubic foot lbft3 equiv lbft3 asymp 1601846337 kgm3

pound (avoirdupois) per cubic inch lbin3 equiv lbin3 asymp 2767990471 times 104 kgm3

pound (avoirdupois) per gallon (Imperial) lbgal equiv lbgal asymp 9977637266 kgm3

pound (avoirdupois) per gallon (US fluid) lbgal equiv lbgal asymp 1198264273 kgm3

slug per cubic foot slugft3 equiv slugft3 asymp 5153788184 kgm3

Time

Time t

Name of unit Symbol Definition Relation to SI units

atomic unit of time au equiv a0(αmiddotc) asymp 2418 884 254times10minus17 s

Callippic cycle equiv 441 mo (hollow) + 499 mo (full) = 76 a of 36525 d = 2398 3776times109 s

century c equiv 100 a (see below for definition of year length) = 100 times year

day d = 24 h = 86400 s

day (sidereal) d equiv Time needed for the Earth to rotate once around its axis determined fromsuccessive transits of a very distant astronomical object across an observersmeridian (International Celestial Reference Frame)

asymp 86 1641 s

decade dec equiv 10 a (see below for definition of year length) = 10 times year

fortnight fn equiv 2 wk = 1 209 600 s

helek equiv 11 080 h = 33 s

Hipparchic cycle equiv 4 Callippic cycles - 1 d = 9593 424times109 s

hour h equiv 60 min = 3 600 s

jiffy j equiv 160 s = 016 s

jiffy (alternate) ja equiv 1100 s = 10 ms

ke (quarter of anhour)

equiv frac14 h = 196 d = 60 times 60 4 s = 900 s = 60 4 min = 15 min

Conversion of units 13

ke (traditional) equiv 1100 d = 24 times 60 times 60 100 s = 864s = 24 60 100 min = 144min

lustre lustrum equiv 5 a of 365 d = 15768times108 s

Metonic cycleenneadecaeteris

equiv 110 mo (hollow) + 125 mo (full) = 6940 d asymp 19 a = 5996 16times108 s

millennium equiv 1 000 a (see below for definition of year length) = 1000 times year

milliday md equiv 11 000 d = 24 times 60 times 60 1 000 s =864 s

minute min equiv 60 s due to leap seconds sometimes 59 s or 61 s = 60 s

moment equiv 90 s = 90 s

month (full) mo equiv 30 d[20] = 2 592 000 s

month (Greg av) mo Average Gregorian month = 365242512 d = 30436875 d asymp 26297times106 s

month (hollow) mo equiv 29 d[20] = 2 505 600 s

month (synodic) mo Cycle time of moon phases asymp 29530589 days (Average) asymp 2551times106 s

octaeteris = 48 mo (full) + 48 mo (hollow) + 3 mo (full)[21] [22] = 8 a of 36525 d = 2922 d = 2524 608times108 s

Planck time equiv (Gℏc5)frac12 asymp 1351 211 868times10minus43 s

second s time of 9 192 631 770 periods of the radiation corresponding to the transitionbetween the 2 hyperfine levels of the ground state of the caesium 133 atom at 0K[8] (but other seconds are sometimes used in astronomy)

(SI base unit)

shake equiv 10minus8 s = 10 ns

sigma equiv 10minus6 s = 1 μs

Sothic cycle equiv 1 461 a of 365 d = 4607 4096times1010 s

svedberg S equiv 10minus13 s = 100 fs

week wk equiv 7 d = 604 800 s

year (Gregorian) a y oryr

= 3652425 d average calculated from common years (365 d) plus leap years (366d) on most years divisible by 4 See leap year for details

= 31 556 952 s

year (Julian) a y oryr

= 36525 d average calculated from common years (365 d) plus one leap year (366d) every four years

= 31 557 600 s

year (sidereal) a y oryr

equiv time taken for Sun to return to the same position with respect to the stars of thecelestial sphere

asymp 365256 363 d asymp 31 5581497632 s

year (tropical) a y oryr

equiv Length of time it takes for the Sun to return to the same position in the cycle ofseasons

asymp 365242 190 d asymp 31 556925 s

Where UTC is observed the length of time units longer than 1 s may increase or decrease by 1 s if a leap second occurs during the time interval ofinterest

Conversion of units 14

Frequency

Frequency

Name of unit Symbol Definition Relation to SI units

hertz (SI unit) Hz equiv Number of cycles per second = 1 Hz = 1s

revolutions per minute rpm equiv One unit rpm equals one rotation completed around a fixed axis in one minute of time asymp 0104719755 rads

Speed or velocity

Speed

Name of unit Symbol Definition Relation to SI units

foot per hour fph equiv 1 fth asymp 8466 667times10minus5 ms

foot per minute fpm equiv 1 ftmin = 508times10minus3 ms

foot per second fps equiv 1 fts = 3048times10minus1 ms

furlong perfortnight

equiv furlongfortnight asymp 1663 095times10minus4 ms

inch per minute ipm equiv 1 inmin asymp 423 333times10minus4 ms

inch per second ips equiv 1 ins = 254times10minus2 ms

kilometre perhour

kmh equiv 1 kmh asymp 2777 778times10minus1 ms

knot kn equiv 1 NMh = 1852 kmh asymp 0514 444 ms

knot (Admiralty) kn equiv 1 NM (Adm)h = 1853 184 kmh = 0514 773 ms

mach number M Ratio of the speed to the speed of sound in the medium Varies especially with temperatureAbout 1225 kmh (761 mph) in air at sea level to about 1062 kmh (660 mph) at jet altitudesUnitless

asymp 340 to 295 ms foraircraft

metre per second(SI unit)

ms equiv 1 ms = 1 ms

mile per hour mph equiv 1 mih = 0447 04 ms

mile per minute mpm equiv 1 mimin = 268224 ms

mile per second mps equiv 1 mis = 1 609344 ms

speed of light invacuum

c equiv 299 792 458 ms = 299 792 458 ms

speed of sound inair

s Varies especially with temperature About 1225 kmh (761 mph) in air at sea level to about1062 kmh (660 mph) at jet altitudes

asymp 340 to 295 ms ataircraft altitudes

A velocity consists of a speed combined with a direction the speed part of the velocity takes units of speed

Conversion of units 15

Flow (volume)

Flow

Name of unit Symbol Definition Relation to SI units

cubic foot per minute CFM equiv 1 ft3min = 4719474432 times 10minus4 m3s

cubic foot per second ft3s equiv 1 ft3s = 0028316846592 m3s

cubic inch per minute in3min equiv 1 in3min = 27311773times10minus7 m3s

cubic inch per second in3s equiv 1 in3s = 16387064 times 10minus5 m3s

cubic metre per second (SI unit) m3s equiv 1 m3s = 1 m3s

gallon (US fluid) per day GPD equiv 1 gald = 4381263638times10minus8 m3s

gallon (US fluid) per hour GPH equiv 1 galh = 1051503273times10minus6 m3s

gallon (US fluid) per minute GPM equiv 1 galmin = 630901964 times 10minus5 m3s

litre per minute LPM equiv 1 Lmin = 16times10minus5 m3s

Acceleration

Acceleration

Name of unit Symbol Definition Relation to SI units

foot per hour per second fphs equiv 1 ft(hmiddots) asymp 8466 667times10minus5 ms2

foot per minute per second fpms equiv 1 ft(minmiddots) = 508times10minus3 ms2

foot per second squared fps2 equiv 1 fts2 = 3048times10minus1 ms2

gal galileo Gal equiv 1 cms2 = 10minus2 ms2

inch per minute per second ipms equiv 1 in(minmiddots) asymp 4233 333times10minus4 ms2

inch per second squared ips2 equiv 1 ins2 = 254times10minus2 ms2

knot per second kns equiv 1 kns asymp 5144 444times10minus1 ms2

metre per second squared (SI unit) ms2 equiv 1 ms2 = 1 ms2

mile per hour per second mphs equiv 1 mi(hmiddots) = 44704times10minus1 ms2

mile per minute per second mpms equiv 1 mi(minmiddots) = 268224 ms2

mile per second squared mps2 equiv 1 mis2 = 1609 344times103 ms2

standard gravity g equiv 9806 65 ms2 = 9806 65 ms2

Conversion of units 16

Force

Force

Name of unit Symbol Definition Relation to SI units

atomic unit of force equiv memiddotα2middotc2a0 asymp 8238 722 06times10minus8 N

[23]

dyne (cgs unit) dyn equiv gmiddotcms2 = 10minus5 N

kilogram-force kilopondgrave-force

kgf kp Gf equiv g times 1 kg = 9806 65 N

kip kip-force kip kipfklbf

equiv g times 1 000 lb = 4448 221 6152605times103 N

milligrave-force gravet-force mGf gf equiv g times 1 g = 9806 65 mN

newton (SI unit) N A force capable of giving a mass of one kg an acceleration of one metreper second per second[24]

= 1 N = 1 kgmiddotms2

ounce-force ozf equiv g times 1 oz = 0278 013 850 9537812 N

pound lb equiv slugmiddotfts2 = 4448 230 531 N

pound-force lbf equiv g times 1 lb = 4448 221 615 2605N

poundal pdl equiv 1 lbmiddotfts2 = 0138 254 954 376 N

sthene (mts unit) sn equiv 1 tmiddotms2 = 1times103 N

ton-force tnf equiv g times 1 sh tn = 8896 443 230521times103 N

See also Conversion between weight (force) and mass

Pressure or mechanical stress

Pressure

Name of unit Symbol Definition Relation to SI units

atmosphere (standard) atm equiv 101 325 Pa [25]

atmosphere (technical) at equiv 1 kgfcm2 = 9806 65times104 Pa [25]

bar bar equiv 105 Pa

barye (cgs unit) equiv 1 dyncm2 = 01 Pa

centimetre of mercury cmHg equiv 13 5951 kgm3 times 1 cm times g asymp 1333 22times103 Pa [25]

centimetre of water (4 degC) cmH2O asymp 999972 kgm3 times 1 cm times g asymp 98063 8 Pa [25]

foot of mercury (conventional) ftHg equiv 13 5951 kgm3 times 1 ft times g asymp 40636 66times103 Pa [25]

foot of water (392 degF) ftH2O asymp 999972 kgm3 times 1 ft times g asymp 2988 98times103 Pa [25]

inch of mercury (conventional) inHg equiv 13 5951 kgm3 times 1 in times g asymp 3386 389times103 Pa [25]

Conversion of units 17

inch of water (392 degF) inH2O asymp 999972 kgm3 times 1 in times g asymp 249082 Pa [25]

kilogram-force per square millimetre kgfmm2 equiv 1 kgfmm2 = 9806 65times106 Pa [25]

kip per square inch ksi equiv 1 kipfsq in asymp 6894 757times106 Pa [25]

micron (micrometre) of mercury mHg equiv 13 5951 kgm3 times 1 m times g asymp 0001 torr asymp 0133 322 4 Pa [25]

millimetre of mercury mmHg equiv 13 5951 kgm3 times 1 mm times g asymp 1 torr asymp 1333224 Pa [25]

millimetre of water (398 degC) mmH2O asymp 999972 kgm3 times 1 mm times g = 0999 972 kgfm2 = 9806 38 Pa

pascal (SI unit) Pa equiv Nm2 = kg(mmiddots2) = 1 Pa [26]

piegraveze (mts unit) pz equiv 1 000 kgmmiddots2 = 1times103 Pa = 1 kPa

pound per square foot psf equiv 1 lbfft2 asymp 47880 26 Pa [25]

pound per square inch psi equiv 1 lbfin2 asymp 6894 757times103 Pa [25]

poundal per square foot pdlsq ft equiv 1 pdlsq ft asymp 1488 164 Pa [25]

short ton per square foot equiv 1 sh tn times g 1 sq ft asymp 95760 518times103 Pa

torr torr equiv 101 325760 Pa asymp 133322 4 Pa [25]

Torque or moment of force

Torque

Name of unit Symbol Definition Relation to SI units

foot-pound force ft lbf equiv g times 1 lb times 1 ft = 1355 817 948 331 4004 Nmiddotm

foot-poundal ft pdl equiv 1 lbmiddotft2s2 = 4214 011 009 380 48times10minus2 Nmiddotm

inch-pound force in lbf equiv g times 1 lb times 1 in = 0112 984 829 027 6167 Nmiddotm

metre kilogram m kg equiv N times m g asymp 0101 971 621 Nmiddotm

Newton metre (SI unit) Nmiddotm equiv N times m = kgmiddotm2s2 = 1 Nmiddotm

Energy work or amount of heat

Energy

Name of unit Symbol Definition Relation to SI units

barrel of oil equivalent bboe asymp 58times106 BTU59 degF asymp 612times109 J

British thermal unit (ISO) BTUISO equiv 10545times103 J = 10545times103 J

British thermal unit (InternationalTable)

BTUIT = 1055 055 852 62times103 J

British thermal unit (mean) BTUmean asymp 1055 87times103 J

British thermal unit(thermochemical)

BTUth asymp 1054 350times103 J

Conversion of units 18

British thermal unit (39 degF) BTU39 degF asymp 1059 67times103 J

British thermal unit (59 degF) BTU59 degF equiv 1054 804times103 J = 1054 804times103 J

British thermal unit (60 degF) BTU60 degF asymp 1054 68times103 J

British thermal unit (63 degF) BTU63 degF asymp 10546times103 J

calorie (International Table) calIT equiv 41868 J = 41868 J

calorie (mean) calmean 1frasl100 of the energy required to warm one gram of air-free waterfrom 0 degC to 100 degC 1 atm

asymp 4190 02 J

calorie (thermochemical) calth equiv 4184 J = 4184 J

calorie (398 degC) cal398 degC asymp 42045 J

calorie (15 degC) cal15 degC equiv 41855 J = 41855 J

calorie (20 degC) cal20 degC asymp 41819 J

Celsius heat unit (InternationalTable)

CHUIT equiv 1 BTUIT times 1 KdegR = 1899 100 534 716times103 J

cubic centimetre of atmospherestandard cubic centimetre

cc atm scc equiv 1 atm times 1 cm3 = 0101 325 J

cubic foot of atmosphere standardcubic foot

cu ft atmscf

equiv 1 atm times 1 ft3 = 2869 204 480 9344times103

J

cubic foot of natural gas equiv 1 000 BTUIT = 1055 055 852 62times106 J

cubic yard of atmosphere standardcubic yard

cu yd atmscy

equiv 1 atm times 1 yd3 = 77468 520 9852288times103 J

electronvolt eV equiv e times 1 V asymp 1602 177 33times10minus19 plusmn49times10minus26 J

erg (cgs unit) erg equiv 1 gmiddotcm2s2 = 10minus7 J

foot-pound force ft lbf equiv g times 1 lb times 1 ft = 1355 817 948 331 4004J

foot-poundal ft pdl equiv 1 lbmiddotft2s2 = 4214 011 009 38048times10minus2 J

gallon-atmosphere (imperial) imp gal atm equiv 1 atm times 1 gal (imp) = 460632 569 25 J

gallon-atmosphere (US) US gal atm equiv 1 atm times 1 gal (US) = 383556 849 0138 J

hartree atomic unit of energy Eh equiv memiddotα2middotc2 (= 2 Ry) asymp 4359 744times10minus18 J

horsepower-hour hpmiddoth equiv 1 hp times 1 h = 2684 519 537 696 172792times106 J

inch-pound force in lbf equiv g times 1 lb times 1 in = 0112 984 829 027 6167J

joule (SI unit) J The work done when a force of one newton moves the point of itsapplication a distance of one metre in the direction of theforce[24]

= 1 J = 1 mmiddotN = 1 kgmiddotm2s2

= 1 CmiddotV = 1 Wmiddots

kilocalorie large calorie kcal Cal equiv 1 000 calIT = 41868times103 J

kilowatt-hour Board of Trade Unit kWmiddothBOTU

equiv 1 kW times 1 h = 36times106 J

Conversion of units 19

litre-atmosphere l atm sl equiv 1 atm times 1 L = 101325 J

quad equiv 1015 BTUIT = 1055 055 852 62times1018 J

rydberg Ry equiv Rinfinmiddotℎmiddotc asymp 2179 872times10minus18 J

therm (EC) equiv 100 000 BTUIT = 105505 585 262times106 J

therm (US) equiv 100 000 BTU59 degF = 1054804times106 J

thermie th equiv 1 McalIT = 41868times106 J

ton of coal equivalent TCE equiv 7 Gcalth = 293076times109 J

ton of oil equivalent TOE equiv 10 Gcalth = 41868times109 J

ton of TNT tTNT equiv 1 Gcalth = 4184times109 J

Power or heat flow rate

Power

Name of unit Symbol Definition Relation to SI units

atmosphere-cubic centimetre perminute

atm ccm equiv 1 atm times 1 cm3min = 1688 75times10minus3 W

atmosphere-cubic centimetre persecond

atm ccs equiv 1 atm times 1 cm3s = 0101 325 W

atmosphere-cubic foot per hour atm cfh equiv 1 atm times 1 cu fth = 0797 001 244 704 W

atmosphere-cubic foot per minute atmmiddotcfm equiv 1 atm times 1 cu ftmin = 47820 074 682 24 W

atmosphere-cubic foot per second atm cfs equiv 1 atm times 1 cu fts = 2869 204 480 9344times103 W

BTU (International Table) per hour BTUITh equiv 1 BTUITh asymp 0293 071 W

BTU (International Table) perminute

BTUITmin equiv 1 BTUITmin asymp 17584 264 W

BTU (International Table) persecond

BTUITs equiv 1 BTUITs = 1055 055 852 62times103 W

calorie (International Table) persecond

calITs equiv 1 calITs = 41868 W

foot-pound-force per hour ft lbfh equiv 1 ft lbfh asymp 3766 161times10minus4 W

foot-pound-force per minute ft lbfmin equiv 1 ft lbfmin = 2259 696 580 552 334times10minus2

W

foot-pound-force per second ft lbfs equiv 1 ft lbfs = 1355 817 948 331 4004 W

horsepower (boiler) bhp asymp 345 lbh times 9703 BTUITlb asymp 9810 657times103 W

horsepower (European electrical) hp equiv 75 kpmiddotms = 736 W

horsepower (Imperial electrical) hp equiv 746 W = 746 W

horsepower (Imperial mechanical) hp equiv 550 ft lbfs = 745699 871 582 270 22 W

horsepower (metric) hp equiv 75 m kgfs = 735498 75 W

litre-atmosphere per minute Lmiddotatmmin equiv 1 atm times 1 Lmin = 1688 75 W

Conversion of units 20

litre-atmosphere per second Lmiddotatms equiv 1 atm times 1 Ls = 101325 W

lusec lusec equiv 1 LmiddotmicromHgs [14] asymp 1333times10minus4 W

poncelet p equiv 100 m kgfs = 980665 W

square foot equivalent directradiation

sq ft EDR equiv 240 BTUITh asymp 70337 057 W

ton of air conditioning equiv 1 t ice melted 24 h asymp 3 504 W

ton of refrigeration (Imperial) equiv 1 BTUIT times 1 lng tnlb divide 10 mins asymp 3938 875times103 W

ton of refrigeration (IT) equiv 1 BTUIT times 1 sh tnlb divide 10 mins asymp 3516 853times103 W

watt (SI unit) W The power which in one second of time gives rise to one jouleof energy[24]

= 1 W = 1 Js = 1 Nmiddotms =1 kgmiddotm2s3

Action

Action

Name of unit Symbol Definition Relation to SI units

atomic unit of action au equiv ℏ equiv ℎ2π asymp 1054 571 68times10minus34 Jmiddots[27]

Dynamic viscosity

Dynamic viscosity

Name of unit Symbol Definition Relation to SI units

pascal second (SI unit) Pamiddots equiv Nmiddotsm2 kg(mmiddots) = 1 Pamiddots

poise (cgs unit) P equiv 10minus1 Pamiddots = 01 Pamiddots

pound per foot hour lb(ftmiddoth) equiv 1 lb(ftmiddoth) asymp 4133 789times10minus4 Pamiddots

pound per foot second lb(ftmiddots) equiv 1 lb(ftmiddots) asymp 1488164 Pamiddots

pound-force second per square foot lbfmiddotsft2 equiv 1 lbfmiddotsft2 asymp 4788026 Pamiddots

pound-force second per square inch lbfmiddotsin2 equiv 1 lbfmiddotsin2 asymp 6894757 Pamiddots

Kinematic viscosity

Conversion of units 21

Kinematic viscosity

Name of unit Symbol Definition Relation to SI units

square foot per second ft2s equiv 1 ft2s = 009290304 m2s

square metre per second (SI unit) m2s equiv 1 m2s = 1 m2s

stokes (cgs unit) St equiv 10minus4 m2s = 10minus4 m2s

Electric current

Electric current

Name of unit Symbol Definition Relation to SI units

ampere (SI base unit) A equiv The constant current needed to produce a force of 2 times10minus7 newton per metre betweentwo straight parallel conductors of infinite length and negligible circular cross-sectionplaced one metre apart in a vacuum[8]

= 1 A

electromagnetic unitabampere (cgs unit)

abamp equiv 10 A = 10 A

esu per secondstatampere (cgs unit)

esus equiv (01 Amiddotms) c asymp3335641 times 10minus10 A

Electric charge

Electric charge

Name of unit Symbol Definition Relation to SI units

abcoulomb electromagnetic unit (cgsunit)

abC emu equiv 10 C = 10 C

atomic unit of charge au equiv e asymp 1602 176462times10minus19 C

coulomb (SI unit) C equiv The amount of electricity carried in one second of time by oneampere of current[24]

= 1 C = 1 Amiddots

faraday F equiv 1 mol times NAmiddote asymp 96 4853383 C

statcoulomb franklin electrostatic unit(cgs unit)

statC Fresu

equiv (01 Amiddotm) c asymp 3335 641times10minus10 C

Electric dipole

Conversion of units 22

Electric dipole

Name of unit Symbol Definition Relation to SI units

atomic unit of electric dipole moment ea0 asymp 8478 352 81times10minus30 Cmiddotm[28]

coulomb meter Cmiddotm = 1 C middot 1 m

debye D = 10minus10 esumiddotAring = 333564095times10minus30 Cmiddotm [29]

Electromotive force electric potential difference

Voltage electromotive force

Name ofunit

Symbol Definition Relation to SI units

abvolt (cgsunit)

abV equiv 1times10minus8 V = 1times10minus8 V

statvolt (cgsunit)

statV equiv cmiddot (1 μJAmiddotm) = 299792 458 V

volt (SIunit)

V The difference in electric potential across two points along a conducting wire carrying one ampereof constant current when the power dissipated between the points equals one watt[24]

= 1 V = 1 WA = 1kgmiddotm2(Amiddots3)

Electrical resistance

Electrical resistance

Name ofunit

Symbol Definition Relation to SI units

ohm (SIunit)

Ω The resistance between two points in a conductor when one volt of electric potential differenceapplied to these points produces one ampere of current in the conductor[24]

= 1 Ω = 1 VA = 1kgmiddotm2(A2middots3)

Capacitance

Capacitors ability to store charge

Name ofunit

Symbol Definition Relation to SI units

farad (SIunit)

F The capacitance between two parallel plates that results in one volt of potential difference whencharged by one coulomb of electricity[24]

= 1 F = 1 CV = 1A2middots4(kgmiddotm2)

Conversion of units 23

Magnetic flux

magnetic flux

Name of unit Symbol Definition Relation to SI units

maxwell (CGSunit)

Mx equiv 10minus8 Wb[30] = 1times10minus8 Wb

weber (SIunit)

Wb Magnetic flux which linking a circuit of one turn would produce in it an electromotive forceof 1 volt if it were reduced to zero at a uniform rate in 1 second[24]

= 1 Wb = 1 Vmiddots = 1kgmiddotm2(Amiddots2)

Magnetic flux density

What physicists call Magnetic field is called Magnetic flux density by electrical engineersand magnetic induction by applied mathematicians and electrical engineers

Name of unit Symbol Definition Relation to SI units

gauss (CGS unit) G equiv Mxcm2 = 10minus4 T = 1times10minus4 T [31]

tesla (SI unit) T equiv Wbm2 = 1 T = 1 Wbm2 = 1 kg(Amiddots2)

Inductance

Inductance

Name ofunit

Symbol Definition Relation to SI units

henry (SIunit)

H The inductance of a closed circuit that produces one volt of electromotive force when the currentin the circuit varies at a uniform rate of one ampere per second[24]

= 1 H = 1 WbA = 1kgmiddotm2(Amiddots)2

Temperature

Temperature

Name of unit Symbol Definition Conversion to kelvin

degree Celsius degC degC equiv K minus 27315 [K] equiv [degC] + 27315

degree Delisle degDe [K] = 37315 minus [degDe] times 23

degree Fahrenheit degF degF equiv degC times 95 + 32 [K] equiv ([degF] + 45967) times 59

degree Newton degN [K] = [degN] times 10033 + 27315

degree Rankine degR degR equiv K times 95 [K] equiv [degR] times 59

degree Reacuteaumur degReacute [K] = [degReacute] times 54 + 27315

degree Roslashmer degRoslash [K] = ([degRoslash] minus 75) times 4021 + 27315

kelvin (SI base unit) K equiv 127316 of the thermodynamic temperature of the triple point of water[8] equiv 1 K

Conversion of units 24

Information entropy

Information entropy

Name of unit Symbol Definition Relation to SI units Relation to bits

SI unit JK equiv JK = 1 JK

nat nip nepit nat equiv kB = 1380 650 5(23)times10minus23 JK

bit shannon bit b Sh equiv ln(2) times kB = 9569 940 (16)times10minus24 JK = 1 bit

ban hartley ban Hart equiv ln(10) times kB = 3179 065 3(53)times10minus23 JK

nibble equiv 4 bits = 3827 976 0(64)times10minus23 JK = 22 bit

byte B equiv 8 bits = 7655 952 (13)times10minus23 JK = 23 bit

kilobyte (decimal) kB equiv 1 000 B = 7655 952 (13)times10minus20 JK = 8times103 bit = 8000 bit

kilobyte (kibibyte) KB KiB equiv 1 024 B = 7839 695 (13)times10minus20 JK = 213 bit = 8192 bit

Often information entropy is measured in shannons whereas the (discrete) storage space of digital devices ismeasured in bits Thus uncompressed redundant data occupy more than one bit of storage per shannon ofinformation entropy The multiples of a bit listed above are usually used with this meaning Other times the bit isused as a measure of information entropy and is thus a synonym of shannon

Luminous intensityThe candela is the preferred nomenclature for the SI unit

Luminous intensity

Name of unit Symbol Definition Relation toSI units

candela (SI baseunit) candle

cd The luminous intensity in a given direction of a source that emits monochromatic radiation offrequency 540times1012 hertz and that has a radiant intensity in that direction of 1683 watt persteradian[8]

= 1 cd

candlepower (new) cp equiv cd The use of candlepower as a unit is discouraged due to its ambiguity = 1 cd

candlepower (oldpre-1948)

cp Varies and is poorly reproducible[32] Approximately 0981 cd[14] asymp 0981 cd

Luminance

Conversion of units 25

Luminance

Name of unit Symbol Definition Relation to SI units

candela per square foot cdft2 equiv cdft2 asymp 10763910417 cdm2

candela per square inch cdin2 equiv cdin2 asymp 15500031 cdm2

candela per square metre (SI unit) nit (deprecated[14] ) cdm2 equiv cdm2 = 1 cdm2

footlambert fL equiv (1π) cdft2 asymp 34262590996 cdm2

lambert L equiv (104π) cdm2 asymp 31830988618 cdm2

stilb (CGS unit) sb equiv 104 cdm2 asymp 1times104 cdm2

Luminous flux

Luminous flux

Name of unit Symbol Definition Relation to SI units

lumen (SI unit) lm equiv cdmiddotsr = 1 lm = 1 cdmiddotsr

Illuminance

Illuminance

Name of unit Symbol Definition Relation to SI units

footcandle lumen per square foot fc equiv lmft2 = 10763910417 lx

lumen per square inch lmin2 equiv lmin2 asymp 15500031 lx

lux (SI unit) lx equiv lmm2 = 1 lx = 1 lmm2

phot (CGS unit) ph equiv lmcm2 = 1times104 lx

Radiation - source activity

Radioactivity

Name of unit Symbol Definition Relation to SI units

becquerel (SI unit) Bq equiv Number of disintegrations per second = 1 Bq = 1s

curie Ci equiv 37times1010 Bq = 37times1010 Bq [33]

rutherford (H) rd equiv 1 MBq = 1times106 Bq

Please note that although becquerel (Bq) and hertz (Hz) both ultimately refer to the same SI base unit (sminus1) Hz isused only for periodic phenomena and Bq is only used for stochastic processes associated with radioactivity[34]

Conversion of units 26

Radiation - exposure

Radiation - exposure

Name of unit Symbol Definition Relation to SI units

roentgen R 1 R equiv 258times10minus4 Ckg[30] = 258times10minus4 Ckg

The roentgen is not a SI unit and the NIST strongly discourages its continued use[35]

Radiation - absorbed dose

Radiation - absorbed dose

Name of unit Symbol Definition Relation to SI units

gray (SI unit) Gy equiv 1 Jkg = 1 m2s2 [36] = 1 Gy

rad rad equiv 001 Gy[30] = 001 Gy

Radiation - equivalent dose

Radiation - equivalent dose

Name of unit Symbol Definition Relation to SI units

Roumlntgen equivalent man rem equiv 001 Sv = 001 Sv

sievert (SI unit) Sv equiv 1 Jkg[34] = 1 Sv

Although the definitions for sievert (Sv) and gray (Gy) would seem to indicate that they measure the same quantitiesthis is not the case The effect of receiving a certain dose of radiation (given as Gy) is variable and depends on manyfactors thus a new unit was needed to denote the biological effectiveness of that dose on the body this is known asthe equivalent dose and is shown in Sv The general relationship between absorbed dose and equivalent dose can berepresented as

H = Q middot D

where H is the equivalent dose D is the absorbed dose and Q is a dimensionless quality factor Thus for anyquantity of D measured in Gy the numerical value for H measured in Sv may be different[37]

Software toolsHome and office computers come with converters in bundled spreadsheet applications or can access free convertersvia the Internet Units and measurements can be easily converted using these tools but only if the units are explicitlydefined and the conversion is compatible (eg cmHg to kPa)

General commercial sources of convertersbull Advanced electronic calculators have unit-conversion functionalitybull Spreadsheet programs usually provide conversion functions or formulas or the user can write their ownbull Commercial mathematical scientific and technical applications often include converters

Conversion of units 27

References[1] United States Naval Observatory (2009) Selected Astronomical Constants 2009 (http asa usno navy mil SecK 2009

Astronomical_Constants_2009 txt) Accessed May 10 2009[2] NIST Reference on Constants Units and Uncertainty (http physics nist gov cgi-bin cuu Valuebohrrada0|search_for=Bohr+

radius)(2006) National Institute of Standards and Technology Retrieved February 22 2008[3] National Institute of Standards and Technology General Tables of Units of Measurement (http ts nist gov WeightsAndMeasures

Publications appxc cfm)[4] Lide D (Ed) (1990) Handbook of Chemistry and Physics (71st ed) Boca Raton FL CRC Press Section 1[5] National Bureau of Standards (June 30 1959) Refinement of values for the yard and the pound Federal Register viewed September 20

2006 at National Geodetic Survey web site (http www ngs noaa gov PUBS_LIB FedRegister FRdoc59-5442 pdf)[6] The International Astronomical Union and Astronomical Units (http www iau org public_press themes measuring )[7] Klein Herbert Arthur (1988) The Science of Measurement a Historical Survey Mineola NY Dover Publications 0-4862-5839-4[8] The International System of Units Section 21 (http www bipm org en si si_brochure chapter2 2-1 ) (8 ed) Bureau International des

Poids et Mesures 2006 retrieved August 26 2009[9] International System of Units (http www bipm org en si si_brochure chapter4 table8 html) 8th ed (2006) Bureau International des

Poids et Mesures Section 41 Table 8[10] P Kenneth Seidelmann Ed (1992) Explanatory Supplement to the Astronomical Almanac Sausalito CA University Science Books p 716

and sv parsec in Glossary[11] Whitelaw Ian (2007) A Measure of All Things The Story of Man and Measurement (http books google com

booksid=3zgGEWM5-iAC) New York Macmillan 0-312-37026-1 p 152[12] De Vinne Theodore Low (1900) The practice of typography a treatise on the processes of type-making the point system the names sizes

styles and prices of plain printing types (http books google com booksid=R4-DjphIpLMC) 2nd ed New York The Century Co p142ndash150

[13] Pasko Wesley Washington (1894) American dictionary of printing and bookmaking (http books google combooksid=Z_QUAAAAIAAJ) (1894) New York Howard Lockwood p 521

[14] Rowlett Russ (2005) How Many A Dictionary of Units of Measurement (http www unc edu ~rowlett units index html)[15] Thompson A and Taylor BN (2008) Guide for the Use of the International System of Units (SI) National Institute of Standards and

Technology Special Publication 811 p 57[16] US Code of Federal Regulations Title 21 Section 1019 Paragraph (b)(5)(viii) (http ecfr gpoaccess gov cgi t text text-idxc=ecframp

rgn=div8amp view=textamp node=212 0 1 1 2 1 1 6amp idno=21) retrieved August 29 2009[17] Barry N Taylor Ed NIST Special Publication 330 The International System of Units (SI) (http physics nist gov Pubs SP330 sp330

pdf) (2001 Edition) Washington US Government Printing Office 43The 12th Conference Generale des Poids et Mesures(CGPM)hellipdeclares that the word ldquolitrerdquo may be employed as a special name for the cubic decimetre

[18] CODATA Value atomic uint of mass (http physics nist gov cgi-bin cuu Valuettme|search_for=atomic+ unit+ of+ mass) (2006)National Institute of Standards and Technology Retrieved 16 September 2008

[19] The Swiss Federal Office for Metrology gives Zentner on a German language web page (http www metas ch de scales systemch html)and quintal on the English translation of that page (http www metas ch en scales systemch html) the unit is marked speacutecifiquementsuisse

[20] Pedersen O (1983) Glossary in Coyne G Hoskin M and Pedersen O Gregorian Reform of the Calendar Proceedings of the VaticanConference to Commemorate its 400th Anniversary Vatican Observatory Available from Astrophysics Data System

[21] Richards EG (1998) Mapping Time Oxford University Press pp 94ndash95 ISBN 0-19-850413-6[22] Steel Duncan (2000) Marking Time John Wiley amp Sons p 46 ISBN 0-471-29827-1[23] CODATA Value atomic unit of force (http physics nist gov cuu Constants ) (2006) National Institute of Standards and Technology

Retrieved September 14 2008[24] [[Comiteacute International des Poids et Mesures (http www bipm org en CIPM db 1946 2 )] Resolution 2] 1946 retrieved August 26

2009[25] Barry N Taylor (April 1 995) Guide for the Use of the International System of Units (SI) (http physics nist gov cuu pdf sp811 pdf)

(NIST Special Publication 811) Washington DC US Government Printing Office pp 57ndash68[26] Barry N Taylor (April 1995) Guide for the Use of the International System of Units (SI) (NIST Special Publication 811) Washington DC

US Government Printing Office p 5[27] International System of Units (http www bipm org en si si_brochure chapter4 table7 html) 8th ed (2006) Bureau International des

Poids et Mesures Section 41 Table 7[28] The NIST Reference on Constants Units and Uncertainty (http physics nist gov cgi-bin cuu Valueauedm) 2006 retrieved August

26 2009[29] Robert G Mortimer Physical chemistryAcademic Press 2000 ISBN 0125083459 page 677[30] NIST Guide to SI Units Appendix B9 (http physics nist gov Pubs SP811 appenB9 html) retrieved August 27 2009[31] Standard for the Use of the International System of Units (SI) The Modern Metric System IEEEASTM SI 10-1997 (1997) New York and

West Conshohocken PA Institute of Electrical and Electronics Engineers and American Society for Testing and Materials Tables A1

Conversion of units 28

through A5[32] The NIST Reference on Constants Units and Uncertainty (http physics nist gov cuu Units candela html) retrieved August 28 2009[33] Ambler Thompson amp Barry N Taylor (2008) Guide for the Use of the International System of Units (SI) (http physics nist gov cuu

pdf sp811 pdf) Special Publication 811 Gaithersburg MD National Institute of Standards and Technology p 10[34] The International System of Units Section 222 Table 3 (http www bipm org en si si_brochure chapter2 2-2 table3 html) (8 ed)

Bureau International des Poids et Mesures 2006 retrieved August 27 2009[35] The NIST Guide to the SI (Special Publication 811) section 52 (http physics nist gov Pubs SP811 sec05 html5 2) 2008 retrieved

August 27 2009[36] Ambler Thompson amp Barry N Taylor (2008) Guide for the Use of the International System of Units (SI) (http physics nist gov cuu

pdf sp811 pdf) Special Publication 811 Gaithersburg MD National Institute of Standards and Technology p 5[37] [[Comiteacute international des poids et mesures (http www bipm org en CIPM db 2002 2 )] 2002 Recommendation 2] retrieved

August 27 2009

External linksbull Official text of the Units of measurement regulations 1995 (http www legislation gov uk uksi 1995 1804

contents made) as createdmade within the United Kingdom from the UK Statute Law Databasebull How Many A dictionary of units of measurement (http www unc edu ~rowlett units )bull NIST Fundamental physical constants mdash Non-SI units (http physics nist gov cuu Document

nonsi_in_1998 pdf)PDF (357 KB)bull NIST Guide to SI Units (http physics nist gov Pubs SP811 appenB9 html) Many conversion factors listedbull The Unified Code for Units of Measure (http aurora rg iupui edu ~schadow units UCUM ucum html)bull Units Symbols and Conversions XML Dictionary (http www posc org refs poscUnits20 xml)bull Units of Measurement Software (http www dmoz org Science Reference Units_of_Measurement Software

) at the Open Directory Projectbull Units of Measurement Online Conversion (http www dmoz org Science Reference Units_of_Measurement

Online_Conversion ) at the Open Directory Project

Article Sources and Contributors 29

Article Sources and ContributorsConversion of units Source httpenwikipediaorgwindexphpoldid=427117714 Contributors 1571781xxx 7 A-giau AVSI Acather96 Ahoerstemeier Alexius08 Altenmann AndreEngels Andrewa Andy120290 Anonymi Ariconte Army1987 ArnoldReinhold Arthur3030 Aspects Avoided AxelBoldt AzaToth Azikala BW95 Bdesham Beland BensaccountBkumartvm Black and White BlaiseFEgan BlueEarth Bobblewik Borbrav Bpmullins Bryan Derksen C J B Scholten CORNELIUSSEON CTZMSC3 Calltech Camerajohn ChaosfearyCharles Matthews Chris the speller Cmdrjameson Colonies Chris Conversion script Cope555 Crappy13 Crissov CyrilB DARTH SIDIOUS 2 DMacks DanielCD Dark FormalDarkestSideX Dekisugi Denelson83 Dhollm Dhp1080 Dicklyon DirkvdM Donarreiskoffer Dramatic Dyss DAringsbquougosz Egil Ehrenkater Ejohnsonboulder Elexmax Elf Emokhberi EnonEob Epbr123 Euchiasmus Fathead99 Father Goose Fella22 Femto FernandoAC Fibula Flutefreek Fred Bauder Fredrik Fuhghettaboutit Funandtrvl Fuzheado Gaff Gene NygaardGeorgiy1996 Gerry Ashton Giftlite Gilliam Glane23 Glenn L GoingBatty Goobergunch Gregsexton Greyengine5 Grunt Gurch Gutza HLHJ Haemo Hammersbach Heracles31 HerbeeHeron HikerBush Hqb Icairns Igiffin Indefatigable Isis JBobbitt JHunterJ Jabowery JakeVortex Jamicanmonkey Jason Begin Jay Jc3s5h Jcronen1 Jdoherty Jef4444 JeffConrad Jeffz1Jeronimo Jimmuhk Jimp Jimwilliams57 Joeinwap Johndburger Josh Parris Jq4bagiq Kaihsu KaneWang Keenan Pepper Kevin Rector KeyStorm Khukri Kurtan Lee Daniel CrockerLightYear LilHelpa Linuxoidoz Liv4christ210 Loggie Lolo252 Lupinelawyer M ichaeligl MJCdetroit MTC Mac MacMcF Mactic Magore Markus Kuhn Masterqwe MaxHundMaxamegalon2000 Mbeychok Mdockrey Meggar Mh26 Michael Daly Michael Hardy Michel Audy Mikelifeguard Mikhailov Kusserow Mindbuilder Monger Mr bulow MrOllieMrZhuKeeper Muro de Aguas Mwanner Mwtoews Nanami Kamimura Nandesuka Natkeeran Ndsg Nfgdayton Ngjaime Nhy67ygv Nick Y Nick123 NickPenguin Ninjagecko NoeNosilleg Now3r3 NuclearEnergy Nudynamik Obelix homologator Oldadamml Oleg Alexandrov Olivier Ortolan88 OwenBlacker Pac72 Passargea Patrick Paul Martin Peter HornPhyschim62 Piels Pierdm Pmanderson Prometheus235 Quadell QuantumEleven Quod erat demonstrandum 314159 Radagast83 Rccoms Reach Out to the Truth RedWolf ReinydayRevipm Rexparry sydney Reyk Rhetth Rhialto Rich Farmbrough Richard Myers Rjwilmsi Rlsheehan Robin Barry RoySmith Rpwolfgram SD6-Agent SGBailey Samuel LowrySamuriSue Samw Sander123 SarahStierch Sdepraz Seabhcan SebastianHelm Sfan00 IMG Shellgirl11355 Sherbert1 Shinhan Shrew Sietse Snel SimonP Sinbaddasail0r Skotte SmalljimSmileyfacegirl1234 SomeHuman Spencer Srleffler StAnselm Starwarsmastergeek Steacoon StefanK SteveRamone Stevertigo Stokerm Suisui Sunev Superboy112233 Superm401Synchronism Tacoman1996 Tarquin Taw Teratornis The Man in Question Thierryc Thingg Thinking of England Thunderbird2 Timwi Tobias Hoevekamp Tomasr Tonsofpcs Toon05Topsykretts2512 Trekphiler Tuwile Twanvl Uday147502 Unitman00 Urhixidur UtherSRG Vargenau Vsmith WarrenPlatts Wasell Welsh Whispering Wikinger Wolfkeeper WtmitchellWtshymanski XJamRastafire Xenonice Yath Zginder Zhou Yu Zibem Zocky Zotel 757 anonymous edits

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