Conversion of Units
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Conversion of Units

Conversion of units is the conversion between different units of measurement for the same quantity, typically through multiplicative conversion factors.

Techniques

Process overview

The process of conversion depends on the specific situation and the intended purpose. This may be governed by regulation, contract, technical specifications or other published standards. Engineering judgment may include such factors as:

Some conversions from one system of units to another need to be exact, without increasing or decreasing the precision of the first measurement. This is sometimes called soft conversion. It does not involve changing the physical configuration of the item being measured.

By contrast, a hard conversion or an adaptive conversion may not be exactly equivalent. It changes the measurement to convenient and workable numbers and units in the new system. It sometimes involves a slightly different configuration, or size substitution, of the item.[clarification needed]Nominal values are sometimes allowed and used.

Conversion factors

A conversion factor is used to change the units of a measured quantity without changing its value. The unity bracket method of unit conversion[1] consists of a fraction in which the denominator is equal to the numerator, but they are in different units. Because of the identity property of multiplication, the value of a quantity will not change as long as it is multiplied by one.[2] Also, if the numerator and denominator of a fraction are equal to each other, then the fraction is equal to one. So as long as the numerator and denominator of the fraction are equivalent, they will not affect the value of the measured quantity.

The following example demonstrates how the unity bracket method is used to convert the rate 5 kilometers per second to meters per second. The symbols km, m, and s represent kilometer, meter, and second, respectively.

Thus, it is found that 5 kilometers per second is equal to 5000 meters per second.

Software tools

There are many conversion tools. They are found in the function libraries of applications such as spreadsheets databases, in calculators, and in macro packages and plugins for many other applications such as the mathematical, scientific and technical applications.

There are many standalone applications that offer the thousands of the various units with conversions. For example, the free software movement offers a command line utility GNU units for Linux and Windows.

Tables of conversion factors

This article gives lists of conversion factors for each of a number of physical quantities, which are listed in the index. For each physical quantity, a number of different units (some only of historical interest) are shown and expressed in terms of the corresponding SI unit. Conversions between units in the metric system are defined by their prefixes (for example, 1 kilogram = 1000 grams, 1 milligram = 0.001 grams) and are thus not listed in this article. Exceptions are made if the unit is commonly known by another name (for example, 1 micron = 10-6 metre). Within each table, the units are listed alphabetically, and the SI units (base or derived) are highlighted.

Legend
Symbol Definition
? exactly equal
? approximately equal to
digits indicates that digits repeat infinitely (e.g. 8.294369 corresponds to 8.294369369369369...)
(H) of chiefly historical interest

Length

Length
Name of unit Symbol Definition Relation to SI units
ångström Å ? ? 0.1 nm
astronomical unit AU ?
? Distance from Earth to Sun
? [3]
attometre am ? ?
barleycorn (H)   = ​ in (see note above about rounding) ? 8.46×10-3 m
bohr, atomic unit of length a0 = Bohr radius of hydrogen ? [4]
cable length (imperial)   ? 608 ft ? 185.3184 m
cable length (International)   ? ​ nmi ? 185.2 m
cable length (US)   ? 720 ft = 219.456 m
chain (Gunter's; Surveyor's) ch ? 66 ft (US) ? 4 rods [5] ?
cubit (H)   ? Distance from fingers to elbow ? 18 in ? 0.5 m
ell (H) ell ? 45 in [6] (In England usually) = 1.143 m
fathom ftm ? 6 ft [6] = 1.8288 m
femtometre fm ? ?
fermi fm ? [6] ?
finger   ? ​ in =
finger (cloth)   ? ​ in = 0.1143 m
foot (Benoît) (H) ft (Ben) ?
foot (Cape) (H)   Legally defined as 1.033 English feet in 1859 ?
foot (Clarke's) (H) ft (Cla) ?
foot (Indian) (H) ft Ind ?
foot, metric mf ? m[] ? 0.31622776602 m
foot, metric (long) lmf ? ​ m ? 0.3 m
foot, metric (short) smf ? 0.30 m ? 0.30 m
foot (International) ft ? 0.3048 m ? ​ yd ? 12 inches ? 0.3048 m
foot (Sear's) (H) ft (Sear) ?
foot (US Survey) ft (US) ? ​ m [7] ?
french; charriere F ? ​ mm = 0.3 ×10-3 m
furlong fur ? 10 chains = 660 ft = 220 yd [6] = 201.168 m
hand   ? 4 in [6] ? 0.1016 m
inch (International) in ? 2.54 cm ? ​ yd ? ​ ft ? 0.0254 m
league (land) lea ? 1 hour walk, Currently defined in US as 3 Statute miles,[5] but historically varied from 2 to 9 km ?
light-day   ? 24 light-hours ?
light-hour   ? 60 light-minutes ?
light-minute   ? 60 light-seconds ?
light-second   ? Distance light travels in one second in vacuum ?
light-year ly ? Distance light travels in vacuum in 365.25 days [8] =
line ln ? ​ in [9] = 0.002116 m
link (Gunter's; Surveyor's) lnk ? ​ ch [6] ? 0.66 ft (US) ? 7.92 in ?
link (Ramsden's; Engineer's) lnk ? 1 ft [6] = 0.3048 m
metre (SI base unit)
(meter)
m ? Distance light travels in ​ of a second in vacuum.[10]
? ​ of the distance from equator to pole.
? 1 m
mickey   ? ​ in =
micrometre (old: micron) μ; μm ? ?
mil; thou mil ? ?
mil (Sweden and Norway) mil ? 10 km =
mile (geographical) (H) ? =
mile (international) mi ? 80 chains ? ? ?
mile (tactical or data) ? ?
mile (telegraph) (H) mi ? =
mile (US Survey) mi ? US Survey feet ? ( × ​) m ?
nail (cloth)   ? ​ in [6] =
nanometre nm ? ?
nautical league NL; nl ? 3 nmi [6] =
nautical mile (Admiralty) NM (Adm); nmi (Adm) = =
nautical mile (international) NM; nmi ? [11] ?
nautical mile (US pre 1954) ? 1853.248 m ? 1853.248 m
pace   ? 2.5 ft [6] = 0.762 m
palm   ? 3 in [6] = 0.0762 m
parsec pc Distant point with a parallax shift of one arc second from a base of one astronomical unit.
? AU[12][13]
? [14]
pica   ? 12 points Dependent on point measures.
picometre pm ? ?
point (American, English)[15][16] pt ? ​ in ?
point (Didot; European) [16][17] pt ? ​ × ​ of pied du roi;

After 1878:
? ​ cm
? ;

After 1878:
?
point (PostScript) [15] pt ? ​ in = 0.0003527 m
point (TeX) [15] pt ? ​ in = 0.0003514598 m
quarter   ? ​ yd = 0.2286 m
rod; pole; perch (H) rd ? ​ ft = 5.0292 m
rope (H) rope ? 20 ft [6] = 6.096 m
shaku (Japan) ? 10/33 m ? 0.303 0303 m
span (H)   ? 9 in [6] = 0.2286 m
spat [18] ?
stick (H)   ? 2 in = 0.0508 m
toise (French, post 1667) (H) T ? 27000/13853 m ? 1.949 0363 m
twip twp ? ​ in = 1.7638×10-5 m
x unit; siegbahn xu ? m [6]
yard (International) yd ? 0.9144 m [7] ? 3 ft ? 36 in ? 0.9144 m
yoctometre ym ? ?
zeptometre zm ? ?

Area

Area
Name of unit Symbol Definition Relation to SI units
acre (international) ac ? = ?
acre (US survey) ac ? 10 sq ch = , also ? [19]
are a ? 100 m2 ? 100 m2
barn b ? 10-28 m2 ? 10-28 m2
barony   ?  ac ?
board bd ? ?
boiler horsepower equivalent direct radiation bhp EDR ? 1 ft2 × 1 bhp / (240 BTUIT/h) ?
circular inch circ in ? ​ sq in ?
circular mil; circular thou circ mil ? ​ mil2 ?
cord   ? 192 bd ?
cuerda (PR Survey) cda ? 1 cda x 1 cda = acre ?
dunam   ? =
guntha (India)   ? 121 sq yd ? 101.17 m2
hectare ha ? ?
hide   ? 120 ac (variable) ?
rood ro ? ​ ac =
ping ? ​ m × ​ m ?
section ? =
shed   ? 10-52 m2 = 10-52 m2
square (roofing) ? =
square chain (international) sq ch ? = ​ ac ?
square chain (US Survey) sq ch ? = ​ US survey acre ?
square foot sq ft ? ?
square foot (US Survey) sq ft ? ?
square inch sq in ? ?
square kilometre km2 ? 1 km × 1 km = 106 m2
square link (Gunter's)(International) sq lnk ? 1 lnk × 1 lnk ? 0.66 ft × 0.66 ft =
square link (Gunter's)(US Survey) sq lnk ? ? ?
square link (Ramsden's) sq lnk ? 1 lnk × 1 lnk ? 1 ft × 1 ft =
square metre (SI unit) m2 ? 1 m × 1 m = 1 m2
square mil; square thou sq mil ? 1 mil × 1 mil =
square mile sq mi ? 1 mi × 1 mi ?
square mile (US Survey) sq mi ? 1 mi (US) × 1 mi (US) ?
square rod/pole/perch sq rd ? 1 rd × 1 rd =
square yard (International) sq yd ? 1 yd × 1 yd ?
stremma   ? =
township   ? 36 sq mi (US) ?
yardland   ? 30 ac ?

Volume

Volume
Name of unit Symbol Definition Relation to SI units
acre-foot ac ft ? 1 ac x 1 ft = =
acre-inch   ? 1 ac × 1 in =
barrel (imperial) bl (imp) ? 36 gal (imp) =
barrel (petroleum); archaic blue-barrel bl; bbl ? 42 gal (US) =
barrel (US dry) bl (US) ? 105 qt (US) = 105/32 bu (US lvl) =
barrel (US fluid) fl bl (US) ? ​ gal (US) =
board-foot fbm ? 144 cu in ?
bucket (imperial) bkt ? 4 gal (imp) =
bushel (imperial) bu (imp) ? 8 gal (imp) =
bushel (US dry heaped) bu (US) ? ​ bu (US lvl) =
bushel (US dry level) bu (US lvl) ? =
butt, pipe   ? 126 gal (wine) =
coomb   ? 4 bu (imp) =
cord (firewood)   ? =
cord-foot   ? 16 cu ft =
cubic fathom cu fm ? 1 fm × 1 fm × 1 fm =
cubic foot ft3 ? 1 ft × 1 ft × 1 ft ?
cubic inch in3 ? 1 in × 1 in × 1 in ?
cubic metre (SI unit) m3 ? 1 m × 1 m × 1 m ? 1 m3
cubic mile cu mi ? 1 mi × 1 mi × 1 mi ?
cubic yard yd3 ? 27 cu ft ?
cup (breakfast)   ? 10 fl oz (imp) =
cup (Canadian) c (CA) ? 8 fl oz (imp) =
cup (metric) c ? =
cup (US customary) c (US) ? 8 US fl oz ? ​ gal (US) =
cup (US food nutrition labeling) c (US) ? 240 mL[20] =
dash (imperial)   ? ​ gi (imp) = ​ pinch (imp) = 369.961751302083×10-9 m3
dash (US)   ? ​ US fl oz = ​ US pinch =
dessertspoon (imperial)   ? ​ gi (imp) = 11.8387760416×10-6 m3
drop (imperial) gtt ? ​ fl oz (imp) = 98.6564670138×10-9 m3
drop (imperial) (alt) gtt ? ​ gi (imp) ?
drop (medical)   ? ​ ml = 83.03×10-9 m3
drop (medical)   ? ​ ml = 83.3×10-9 m3
drop (metric)   ? ​ mL =
drop (US) gtt ? ​ US fl oz = 82.14869322916×10-9 m3
drop (US) (alt) gtt ? ​ US fl oz ?
drop (US) (alt) gtt ? ​ US fl oz ?
fifth   ? ​ US gal =
firkin   ? 9 gal (imp) =
fluid drachm (imperial) fl dr ? ​ fl oz (imp) =
fluid dram (US); US fluidram fl dr ? ​ US fl oz =
fluid scruple (imperial) fl s ? ​ fl oz (imp) = 1.18387760416×10-6 m3
gallon (beer) beer gal ? 282 cu in =
gallon (imperial) gal (imp) ? ?
gallon (US dry) gal (US) ? ​ bu (US lvl) =
gallon (US fluid; Wine) gal (US) ? 231 cu in ?
gill (imperial); Noggin gi (imp); nog ? 5 fl oz (imp) =
gill (US) gi (US) ? 4 US fl oz =
hogshead (imperial) hhd (imp) ? 2 bl (imp) =
hogshead (US) hhd (US) ? 2 fl bl (US) =
jigger (bartending)   ? ​ US fl oz ?
kilderkin   ? 18 gal (imp) =
lambda ? ? 1 mm3 =
last   ? 80 bu (imp) =
litre
(liter)
L ? 1 dm3[21] ? 0.001 m3
load   ? 50 cu ft =
minim (imperial) min ? ​ fl oz (imp) = 1/60 fl dr (imp) = 59.1938802083×10-9 m3
minim (US) min ? ​ US fl oz = ​ US fl dr =
ounce (fluid imperial) fl oz (imp) ? ​ gal (imp) ?
ounce (fluid US customary) US fl oz ? ​ gal (US) ?
ounce (fluid US food nutrition labeling) US fl oz ? 30 mL[20] ?
peck (imperial) pk ? 2 gal (imp) =
peck (US dry) pk ? ​ US lvl bu =
perch per ? =
pinch (imperial)   ? ​ gi (imp) = 1/16 tsp (imp) = 739.92350260416×10-9 m3
pinch (US)   ? ​ US fl oz = 1/16 US tsp =
pint (imperial) pt (imp) ? ​ gal (imp) =
pint (US dry) pt (US dry) ? ​ bu (US lvl) ? ​ gal (US dry) =
pint (US fluid) pt (US fl) ? ​ gal (US) =
pony   ? ​ US fl oz =
pottle; quartern   ? ​ gal (imp) = 80 fl oz (imp) =
quart (imperial) qt (imp) ? ​ gal (imp) =
quart (US dry) qt (US) ? ​ bu (US lvl) = ​ gal (US dry) =
quart (US fluid) qt (US) ? ​ gal (US fl) =
quarter; pail   ? 8 bu (imp) =
register ton   ? 100 cu ft =
sack (US)   ? 3 bu (US lvl) =
seam   ? 8 bu (US lvl)[] =
shot (US)   usually 1.5 US fl oz[18] ?
strike (imperial)   ? 2 bu (imp) =
strike (US)   ? 2 bu (US lvl) =
tablespoon (Australian metric)   ?
tablespoon (Canadian) tbsp ? ​ fl oz (imp) =
tablespoon (imperial) tbsp ? ​ fl oz (imp) =
tablespoon (metric)   ?
tablespoon (US customary) tbsp ? ​ US fl oz =
tablespoon (US food nutrition labeling) tbsp ? 15 mL[20] =
teaspoon (Canadian) tsp ? ​ fl oz (imp) = 4.735510416×10-6 m3
teaspoon (imperial) tsp ? ​ gi (imp) = 5.91938802083×10-6 m3
teaspoon (metric)   ? =
teaspoon (US customary) tsp ? ​ US fl oz =
teaspoon (US food nutrition labeling) tsp ? 5 mL[20] =
timber foot   ? 1 cu ft =
ton (displacement)   ? 35 cu ft =
ton (freight)   ? 40 cu ft =
ton (water)   ? 28 bu (imp) =
tun   ? 252 gal (wine) =
wey (US)   ? 40 bu (US lvl) =

Plane angle

Plane angle
Name of unit Symbol Definition Relation to SI units
angular mil µ ? ​ rad ?
arcminute; MOA ' ? ​ ?
arcsecond " ? ​ ?
centesimal minute of arc ' ? ​ grad ?
centesimal second of arc " ? ​ grad ?
degree (of arc) ° ? ​ of a revolution ? ​ rad ?
grad; gradian; gon grad ? ​ of a revolution ? ​ rad ? 0.9°
octant   ? 45° ?
quadrant   ? 90° ?
radian (SI unit) rad The angle subtended at the center of a circle by

an arc whose length is equal to the circle's radius.
One full revolution encompasses 2? radians.

= 1 rad
sextant   ? 60° ?
sign   ? 30° ?

Solid angle

Solid angle
Name of unit Symbol Definition Relation to SI units
spat [18] - The solid angle subtended by a sphere at its centre. ?
square degree deg2; sq.deg.; (°)2
steradian (SI unit) sr The solid angle subtended at the center of a sphere of radius r

by a portion of the surface of the sphere having an area r2.
A sphere subtends 4? sr.[18]

= 1 sr

Mass

Notes:

  • See Weight for detail of mass/weight distinction and conversion.
  • Avoirdupois is a system of mass based on a pound of 16 ounces, while Troy weight is the system of mass where 12 troy ounces equals one troy pound.
  • In this table, the unit gee is used to denote standard gravity in order to avoid confusion with the "g" symbol for grams.
Mass
Name of unit Symbol Definition Relation to SI units
atomic mass unit, unified u; AMU Same as dalton (see below) ? [22]
atomic unit of mass, electron rest mass me ? [23]
bag (coffee)   ? 60 kg = 60 kg
bag (Portland cement)   ? 94 lb av =
barge   ? ​ short ton =
carat kt ? ​ gr = 3 mg
carat (metric) ct ? 200 mg = 200 mg
clove   ? 8 lb av =
crith   ? mass of 1 L of hydrogen gas at STP ? 89.9349 mg
dalton Da 1/12 the mass of an unbound neutral atom of
carbon-12 in its nuclear and electronic
ground state and at rest
? [22]
dram (apothecary; troy) dr t ? 60 gr =
dram (avoirdupois) dr av ? ​ gr =
electronvolt eV ? 1 eV (energy unit) / c2 = [24]
gamma ? ? 1 ?g = 1 ?g
grain gr ? ​ lb av ?
grave gv. grave was the original name of the kilogram ? 1 kg
hundredweight (long) long cwt or cwt ? 112 lb av =
hundredweight (short); cental sh cwt ? 100 lb av =
kilogram
(kilogramme)
kg ? mass of the prototype near Paris
? mass of 1 litre of water
? 1 kg (SI base unit)[10]
kip kip ? av =
mark   ? 8 oz t =
mite   ? ​ gr =
mite (metric)   ? ​ g = 50 mg
ounce (apothecary; troy) oz t ? ​ lb t =
ounce (avoirdupois) oz av ? ​ lb =
ounce (US food nutrition labelling) oz ? 28 g[20] = 28 g
pennyweight dwt; pwt ? ​ oz t =
point   ? ​ ct = 2 mg
pound (avoirdupois) lb av ? = grains ?
pound (metric)   ? 500 g = 500 g
pound (troy) lb t ? grains =
quarter (imperial)   ? ​ long cwt = 2 st = 28 lb av =
quarter (informal)   ? ​ short ton =
quarter, long (informal)   ? ​ long ton =
quintal (metric) q ? 100 kg = 100 kg
scruple (apothecary) s ap ? 20 gr =
sheet   ? ​ lb av = 647.9891 mg
slug; geepound; hyl slug ? 1 ɡ0 × 1 lb av × 1 s2/ft ?
stone st ? 14 lb av =
ton, assay (long) AT ? 1 mg × 1 long ton ÷ 1 oz t = 32.6 g
ton, assay (short) AT ? 1 mg × 1 short ton ÷ 1 oz t = 29.16 g
ton, long long tn or ton ? =
ton, short sh tn ? =
tonne (mts unit) t ? =
wey   ? 252 lb = 18 st = (variants exist)
Zentner Ztr. Definitions vary.[18][25]

Density

Density
Name of unit Symbol Definition Relation to SI units
gram per millilitre g/mL ? g/mL =
kilogram per cubic metre (SI unit) kg/m3 ? kg/m3 = 1 kg/m3
kilogram per litre kg/L ? kg/L =
ounce (avoirdupois) per cubic foot oz/ft3 ? oz/ft3 ?
ounce (avoirdupois) per cubic inch oz/in3 ? oz/in3 ?
ounce (avoirdupois) per gallon (imperial) oz/gal ? oz/gal ?
ounce (avoirdupois) per gallon (US fluid) oz/gal ? oz/gal ?
pound (avoirdupois) per cubic foot lb/ft3 ? lb/ft3 ?
pound (avoirdupois) per cubic inch lb/in3 ? lb/in3 ?
pound (avoirdupois) per gallon (imperial) lb/gal ? lb/gal ?
pound (avoirdupois) per gallon (US fluid) lb/gal ? lb/gal ?
slug per cubic foot slug/ft3 ? slug/ft3 ?

Time

Time
Name of unit Symbol Definition Relation to SI units
Atomic unit of time au ? a0/(?·c) ?
Callippic cycle   ? 441 mo (hollow) + 499 mo (full) = 76 a of 365.25 d = or [note 1]
Century c ? 100 years (100 a) [note 2][note 3]
Day d = 24 h = min = [note 3]
Day (sidereal) d ? Time needed for the Earth to rotate once around its axis, determined from successive transits of a very distant astronomical object across an observer's meridian (International Celestial Reference Frame) ?
Decade dec ? 10 years (10 a) = [note 2][note 3]
Fortnight fn ? 2 wk = [note 3]
Helek ? ​ h = 3.3 s
Hipparchic cycle   ? 4 Callippic cycles - 1 d =
Hour h ? 60 min = [note 3]
Jiffy j ? ​ s = 16.6 ms
Jiffy (alternative) ja ? ​ s = 10 ms
Ke (quarter of an hour)   ? ​ h = ​ d = 15 min = 900 s
Ke (traditional)   ? ​ d = 14.4 min = 864 s
Lustre; Lustrum   ? 5 a of 365 d[note 4] =
Metonic cycle; enneadecaeteris   ? 110 mo (hollow) + 125 mo (full) = 6940 d ? 19 a =
Millennium   ? years [note 2][note 3]
Milliday md ? ​ d = 86.4 s
Minute min ? 60 s, due to leap seconds sometimes 59 s or 61 s, = 60 s[note 3]
Moment   ? 90 s = 90 s
Month (full) mo ? 30 d[26] = [note 3]
Month (Greg. av.) mo = ? [note 3]
Month (hollow) mo ? 29 d[26] = [note 3]
Month (synodic) mo Cycle time of moon phases ? (average) ?
Octaeteris   = 48 mo (full) + 48 mo (hollow) + 3 mo (full)[27][28] = 8 a of 365.25 d = 2922 d = [note 3]
Planck time   ? (​) ? [29]
Second s Time of periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom at 0 K[10] (but other seconds are sometimes used in astronomy). Also that time it takes for light to travel a distance of metres. (SI base unit)
Shake   ? 10-8 s = 10 ns
Sigma   ? 10-6 s = 1 ?s
Sothic cycle   ? a of 365 d =
Svedberg S ? 10-13 s = 100 fs
Week wk ? 7 d = 168 h = = [note 3]
Year (common) 365 d = [note 3][note 3][30]
Year (Gregorian) a, y, or yr = 365.2425 d average, calculated from common years (365 d) plus leap years (366 d) on most years divisible by 4. See leap year for details. = [note 3]
Year (Julian) a, y, or yr = 365.25 d average, calculated from common years (365 d) plus one leap year (366 d) every four years =
Year (leap) a, y, or yr 366 d = [note 3][30]
Year (mean tropical) a, y, or yr Conceptually, the length of time it takes for the Sun to return to the same position in the cycle of seasons, [Converter 1] approximately d, each day being SI seconds[31] ?
Year (sidereal) a, y, or yr ? Time taken for Sun to return to the same position with respect to the stars of the celestial sphere, approximately ?
Notes:
  1. ^ see Callippic cycle for explanation of the differences
  2. ^ a b c This is based on the average Gregorian year. See above for definition of year lengths.
  3. ^ a b c d e f g h i j k l m n o p Where UTC is observed, the length of this unit may increase or decrease
    depending on the number of leap seconds which occur during the time interval in question.
  4. ^ The length of ancient lustral cycles was not constant; see Lustrum for more details

Frequency

Frequency
Name of unit Symbol Definition Relation to SI units
hertz (SI unit) Hz ? Number of cycles per second = 1 Hz = 1/s
revolutions per minute rpm ? One unit rpm equals one rotation completed around a fixed axis in one minute of time. ?

Speed or velocity

Speed
Name of unit Symbol Definition Relation to SI units
foot per hour fph ? 1 ft/h = 8.46×10-5 m/s
foot per minute fpm ? 1 ft/min =
foot per second fps ? 1 ft/s =
furlong per fortnight   ? furlong/fortnight ?
inch per hour iph ? 1 in/h = 7.05×10-6 m/s
inch per minute ipm ? 1 in/min = 4.23×10-4 m/s
inch per second ips ? 1 in/s =
kilometre per hour km/h ? 1 km/h = 2.7×10-1 m/s
knot kn ? 1 nmi/h = 1.852 km/h = 0.514 m/s
knot (Admiralty) kn ? 1 NM (Adm)/h = [] = 3 m/s
mach number M Ratio of the speed to the speed of sound[note 1] in the medium (unitless). ? 340 to 295 m/s
metre per second (SI unit) m/s ? 1 m/s = 1 m/s
mile per hour mph ? 1 mi/h =
mile per minute mpm ? 1 mi/min =
mile per second mps ? 1 mi/s =
speed of light in vacuum c ? =
speed of sound in air s to (761-660 mph or 661-574 kn)[note 1] ?
Note
  1. ^ a b The speed of sound varies especially with temperature and pressure from about (761 mph or 661 kn)
    in air at sea level to about (660 mph or 570 kn) at jet altitudes (12200 m or 40000 ft).[32]

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

Flow (volume)

Flow
Name of unit Symbol Definition Relation to SI units
cubic foot per minute CFM[] ? 1 ft3/min =
cubic foot per second ft3/s ? 1 ft3/s =
cubic inch per minute in3/min ? 1 in3/min = 3×10-7 m3/s
cubic inch per second in3/s ? 1 in3/s =
cubic metre per second (SI unit) m3/s ? 1 m3/s = 1 m3/s
gallon (US fluid) per day GPD[] ? 1 gal/d = 8×10-8 m3/s
gallon (US fluid) per hour GPH[] ? 1 gal/h = 3×10-6 m3/s
gallon (US fluid) per minute GPM[] ? 1 gal/min =
litre per minute LPM[] ? 1 L/min = 1.6×10-5 m3/s

Acceleration

Acceleration
Name of unit Symbol Definition Relation to SI units
foot per hour per second fph/s ? 1 ft/(h·s) = 8.46×10-5 m/s2
foot per minute per second fpm/s ? 1 ft/(min·s) =
foot per second squared fps2 ? 1 ft/s2 =
gal; galileo Gal ? 1 cm/s2 = 10-2 m/s2
inch per minute per second ipm/s ? 1 in/(min·s) = 4.23×10-4 m/s2
inch per second squared ips2 ? 1 in/s2 =
knot per second kn/s ? 1 kn/s ? 5.14×10-1 m/s2
metre per second squared (SI unit) m/s2 ? 1 m/s2 = 1 m/s2
mile per hour per second mph/s ? 1 mi/(h·s) =
mile per minute per second mpm/s ? 1 mi/(min·s) = 26.8224 m/s2
mile per second squared mps2 ? 1 mi/s2 =
standard gravity ɡ0 ? =

Force

Force
Name of unit Symbol Definition Relation to SI units
atomic unit of force ? ​ ? [33]
dyne (cgs unit) dyn ? g·cm/s2 = 10-5 N
kilogram-force; kilopond; grave-force kgf; kp; Gf ? ɡ0 × 1 kg =
kip; kip-force kip; kipf; klbf ? ɡ0 × =
milligrave-force, gravet-force mGf; gf ? ɡ0 × 1 g =
long ton-force tnf[] ? ɡ0 × 1 long ton =
newton (SI unit) N A force capable of giving a mass of one kilogram an acceleration of one metre per second per second.[34] = 1 N = 1 kg·m/s2
ounce-force ozf ? ɡ0 × 1 oz =
pound-force lbf ? ɡ0 × 1 lb =
poundal pdl ? 1 lb·ft/s2 =
short ton-force tnf[] ? ɡ0 × 1 short ton =
sthene (mts unit) sn ? 1 t·m/s2 = 103 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 ? [35]
atmosphere (technical) at ? 1 kgf/cm2 = [35]
bar bar ? 105 Pa
barye (cgs unit)   ? 1 dyn/cm2 = 0.1 Pa
centimetre of mercury cmHg ? × 1 cm × ɡ0 ? [35]
centimetre of water (4 °C) cmH2O ? 999.972 kg/m3 × 1 cm × ɡ0 ? [35]
foot of mercury (conventional) ftHg ? × 1 ft × ɡ0 ? [35]
foot of water (39.2 °F) ftH2O ? 999.972 kg/m3 × 1 ft × ɡ0 ? [35]
inch of mercury (conventional) inHg ? × 1 in × ɡ0 ? [35]
inch of water (39.2 °F) inH2O ? 999.972 kg/m3 × 1 in × ɡ0 ? [35]
kilogram-force per square millimetre kgf/mm2 ? 1 kgf/mm2 = [35]
kip per square inch ksi ? 1 kipf/sq in ? [35]
long ton per square foot   ? 1 long ton × ɡ0 / 1 sq ft ?
micrometre of mercury μmHg ? × 1 μm × ɡ0 ? 0.001 torr ? [35]
millimetre of mercury mmHg ? × 1 mm × ɡ0 ? 1 torr ? [35]
millimetre of water (3.98 °C) mmH2O ? 999.972 kg/m3 × 1 mm × ɡ0 = =
pascal (SI unit) Pa ? N/m2 = kg/(m·s2) = 1 Pa[36]
pièze (mts unit) pz ? = = 1 kPa
pound per square foot psf ? 1 lbf/ft2 ? [35]
pound per square inch psi ? 1 lbf/in2 ? [35]
poundal per square foot pdl/sq ft ? 1 pdl/sq ft ? [35]
short ton per square foot   ? 1 short ton × ɡ0 / 1 sq ft ?
torr torr ? ​ Pa ? [35]

Torque or moment of force

Torque
Name of unit Symbol Definition Relation to SI units
pound-force-foot lbfoft ? ɡ0 × 1 lb × 1 ft =
poundal-ft pdloft ? 1 lb·ft2/s2 =
pound force-inch lbfoin ? ɡ0 × 1 lb × 1 in =
kilogram force-meter kgfom ? ɡ0 × N × m =
Newton metre (SI unit) N·m ? N × m = kg·m2/s2 =

Energy

Energy
Name of unit Symbol Definition Relation to SI units
barrel of oil equivalent boe ? ?
British thermal unit (ISO) BTUISO ? =
British thermal unit (International Table) BTUIT =
British thermal unit (mean) BTUmean ?
British thermal unit (thermochemical) BTUth ?
British thermal unit (39 °F) BTU39 °F ?
British thermal unit (59 °F) BTU59 °F ? =
British thermal unit (60 °F) BTU60 °F ?
British thermal unit (63 °F) BTU63 °F ?
calorie (International Table) calIT ? =
calorie (mean) calmean ​ of the energy required to warm one gram of air-free water from 0 °C to 100 °C at a pressure of 1 atm ?
calorie (thermochemical) calth ? 4.184 J =
Calorie (US; FDA) Cal ? 1 kcal = =
calorie (3.98 °C) cal3.98 °C ?
calorie (15 °C) cal15 °C ? 4.1855 J =
calorie (20 °C) cal20 °C ?
Celsius heat unit (International Table) CHUIT ? 1 BTUIT × 1 K/°R =
cubic centimetre of atmosphere; standard cubic centimetre cc atm; scc ? 1 atm × 1 cm3 =
cubic foot of atmosphere; standard cubic foot cu ft atm; scf ? 1 atm × 1 ft3 =
cubic foot of natural gas   ? =
cubic yard of atmosphere; standard cubic yard cu yd atm; scy ? 1 atm × 1 yd3 =
electronvolt eV ? e × 1 V ?
erg (cgs unit) erg ? 1 g·cm2/s2 = 10-7 J
foot-pound force ft lbf ? ɡ0 × 1 lb × 1 ft =
foot-poundal ft pdl ? 1 lb·ft2/s2 =
gallon-atmosphere (imperial) imp gal atm ? 1 atm × 1 gal (imp) =
gallon-atmosphere (US) US gal atm ? 1 atm × 1 gal (US) =
hartree, atomic unit of energy Eh ? me·?2·c2 (= 2 Ry) ?
horsepower-hour hp·h ? 1 hp × 1 h =
inch-pound force in lbf ? ɡ0 × 1 lb × 1 in =
joule (SI unit) J The work done when a force of one newton moves the point of its application a distance of one metre in the direction of the force.[34] = 1 J = 1 m·N = 1 kg·m2/s2 = 1 C·V = 1 W·s
kilocalorie; large calorie kcal; Cal ? =
kilowatt-hour; Board of Trade Unit kW·h; B.O.T.U. ? 1 kW × 1 h =
litre-atmosphere l atm; sl ? 1 atm × 1 L =
quad   ? 1015 BTUIT =
rydberg Ry ? R?·h·c ?
therm (E.C.)   ? =
therm (US)   ? =
thermie th ? 1 McalIT =
ton of coal equivalent TCE ? 7 Gcalth =
tonne of oil equivalent toe ? 10 GcalIT =
ton of TNT tTNT ? 1 Gcalth =

Power or heat flow rate

Power
Name of unit Symbol Definition Relation to SI units
atmosphere-cubic centimetre per minute atm ccm[] ? 1 atm × 1 cm3/min =
atmosphere-cubic centimetre per second atm ccs[] ? 1 atm × 1 cm3/s =
atmosphere-cubic foot per hour atm cfh[] ? 1 atm × 1 cu ft/h =
atmosphere-cubic foot per minute atm cfm[] ? 1 atm × 1 cu ft/min =
atmosphere-cubic foot per second atm cfs[] ? 1 atm × 1 cu ft/s =
BTU (International Table) per hour BTUIT/h ? 1 BTUIT/h ?
BTU (International Table) per minute BTUIT/min ? 1 BTUIT/min ?
BTU (International Table) per second BTUIT/s ? 1 BTUIT/s =
calorie (International Table) per second calIT/s ? 1 calIT/s =
erg per second erg/s ? 1 erg/s =
foot-pound-force per hour ft·lbf/h ? 1 ft lbf/h ?
foot-pound-force per minute ft·lbf/min ? 1 ft lbf/min =
foot-pound-force per second ft·lbf/s ? 1 ft lbf/s =
horsepower (boiler) hp ? 34.5 lb/h × 970.3 BTUIT/lb ? [37]
horsepower (European electrical) hp ? 75 kp·m/s = []
horsepower (electrical) hp ? 746 W = [37]
horsepower (mechanical) hp ? 550 ft·lbf/s[37] =
horsepower (metric) hp or PS ? 75 m·kgf/s = [37]
litre-atmosphere per minute L·atm/min ? 1 atm × 1 L/min =
litre-atmosphere per second L·atm/s ? 1 atm × 1 L/s =
lusec lusec ? 1 L·µmHg/s [18] ?
poncelet p ? 100 m·kgf/s =
square foot equivalent direct radiation sq ft EDR ? 240 BTUIT/h ?
ton of air conditioning   ? of ice melted / 24 h ?
ton of refrigeration (imperial)   ? × iceIT / 24 h: iceIT = 144 °F × 2326 J/kg·°F ?
ton of refrigeration (IT)   ? × iceIT / 24 h: iceIT = 144 °F × 2326 J/kg·°F ?
watt (SI unit) W The power which in one second of time gives rise to one joule of energy.[34] = = 1 J/s = 1 N·m/s = 1 kg·m2/s3

Action

Action
Name of unit Symbol Definition Relation to SI units
atomic unit of action au ? ? ? ​ ? [38]

Dynamic viscosity

Dynamic viscosity
Name of unit Symbol Definition Relation to SI units
pascal second (SI unit) Pa·s ? N·s/m2, kg/(m·s) = 1 Pa·s
poise (cgs unit) P ? 1 barye·s = 0.1 Pa·s
pound per foot hour lb/(ft·h) ? 1 lb/(ft·h) ?
pound per foot second lb/(ft·s) ? 1 lb/(ft·s) ?
pound-force second per square foot lbf·s/ft2 ? 1 lbf·s/ft2 ?
pound-force second per square inch lbf·s/in2 ? 1 lbf·s/in2 ?

Kinematic viscosity

Kinematic viscosity
Name of unit Symbol Definition Relation to SI units
square foot per second ft2/s ? 1 ft2/s =
square metre per second (SI unit) m2/s ? 1 m2/s = 1 m2/s
stokes (cgs unit) St ? 1 cm2/s = 10-4 m2/s

Electric current

Electric current
Name of unit Symbol Definition Relation to SI units
ampere (SI base unit) A ? The constant current needed to produce a force of 2 ×10-7 newton per metre between two straight parallel conductors of infinite length and negligible circular cross-section placed one metre apart in a vacuum.[10] = 1 A = 1 C/s
electromagnetic unit; abampere (cgs unit) abamp ? 10 A = 10 A
esu per second; statampere (cgs unit) esu/s ? ​ ?

Electric charge

Electric charge
Name of unit Symbol Definition Relation to SI units
abcoulomb; electromagnetic unit (cgs unit) abC; emu ? 10 C = 10 C
atomic unit of charge au ? e ?
coulomb C ? The amount of electricity carried in one second of time by one ampere of current.[34] = 1 C = 1 A·s
faraday F ? 1 mol × NA·e ?
milliampere hour mA·h ? 0.001 A × 1 h = 3.6 C
statcoulomb; franklin; electrostatic unit (cgs unit) statC; Fr; esu ? ​ ?

Electric dipole

Electric dipole
Name of unit Symbol Definition Relation to SI units
atomic unit of electric dipole moment ea0   ? [39]
coulomb meter C·m   = 1 C · 1 m
debye D = 10-10 esu·Å = [40]

Electromotive force, electric potential difference

Voltage, electromotive force
Name of unit Symbol Definition Relation to SI units
abvolt (cgs unit) abV ? 10-8 V = 10-8 V
statvolt (cgs unit) statV ? c·(1 ?J/A·m) =
volt (SI unit) V The difference in electric potential across two points along a conducting wire carrying one ampere of constant current when the power dissipated between the points equals one watt.[34] = 1 V = 1 W/A

Electrical resistance

Electrical resistance
Name of unit Symbol Definition Relation to SI units
ohm (SI unit) ? The resistance between two points in a conductor when one volt of electric potential difference, applied to these points, produces one ampere of current in the conductor.[34] = 1 ? = 1 V/A

Capacitance

Capacitor's ability to store charge
Name of unit Symbol Definition Relation to SI units
farad (SI unit) F The capacitance between two parallel plates that results in one volt of potential difference when charged by one coulomb of electricity.[34] = 1 F = 1 C/V

Magnetic flux

magnetic flux
Name of unit Symbol Definition Relation to SI units
maxwell (CGS unit) Mx ? 10-8 Wb[37] = 10-8 Wb
weber (SI unit) Wb Magnetic flux which, linking a circuit of one turn, would produce in it an electromotive force of 1 volt if it were reduced to zero at a uniform rate in 1 second.[34] = 1 Wb = 1 V·s

Magnetic flux density

What physicists call Magnetic field is called Magnetic flux density by electrical engineers and magnetic induction by applied mathematicians and electrical engineers.
Name of unit Symbol Definition Relation to SI units
gauss (CGS unit) G ? Mx/cm2 = 10-4 T = 10-4 T [41]
tesla (SI unit) T ? Wb/m2 = 1 T = 1 Wb/m2

Inductance

Inductance
Name of unit Symbol Definition Relation to SI units
henry (SI unit) H The inductance of a closed circuit that produces one volt of electromotive force when the current in the circuit varies at a uniform rate of one ampere per second.[34] = 1 H = 1 Wb/A

Temperature

Temperature
Name of unit Symbol Definition Relation to SI units
degree Celsius °C [°C] ? [K] - 273.15 [K] ? [°C] + 273.15
degree Delisle °De [K] = 373.15 - [°De] × ​
degree Fahrenheit °F [°F] ? [°C] × ​ + 32 [K] ? ([°F] + 459.67) × ​
degree Newton °N [K] = [°N] × ​ + 273.15
degree Rankine °R; [°R] ? [K] × ​ [K] ? [°R] × 5/9
degree Réaumur °Ré [K] = [°Ré] × ​ + 273.15
degree Rømer °Rø [K] = ([°Rø] - 7.5) × ​ + 273.15
Regulo Gas Mark GM; [°F] ? [GM] × 25 + 300 [K] ? [GM] × ​ + 422.038
kelvin (SI base unit) K ? ​ of the thermodynamic temperature of the triple point of water.[10] ? 1 K

Information entropy

Information entropy
Name of unit Symbol Definition Relation to SI units Relation to bits
natural unit of information; nip; nepit nat
shannon; bit Sh; bit; b ? ln(2) × nat ? = 1 bit
hartley; ban Hart; ban ? ln(10) × nat ?
nibble ? 4 bits = 22 bit
byte B ? 8 bits = 23 bit
kilobyte (decimal) kB ? = bit
kilobyte (kibibyte) KB; KiB ? = 213 bit = bit

Modern standards (such as ISO 80000) prefer the shannon to the bit as a unit for a quantity of information entropy, whereas the (discrete) storage space of digital devices is measured in bits. Thus, uncompressed redundant data occupy more than one bit of storage per shannon of information entropy. The multiples of a bit listed above are usually used with this meaning.

Luminous intensity

The candela is the preferred nomenclature for the SI unit.

Luminous intensity
Name of unit Symbol Definition Relation to SI units
candela (SI base unit); candle cd The luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency 540×1012 hertz and that has a radiant intensity in that direction of 1/683 watt per steradian.[10] = 1 cd
candlepower (new) cp ? cd The use of candlepower as a unit is discouraged due to its ambiguity. = 1 cd
candlepower (old, pre-1948) cp Varies and is poorly reproducible.[42] Approximately 0.981 cd.[18] ? 0.981 cd

Luminance

Luminance
Name of unit Symbol Definition Relation to SI units
candela per square foot cd/ft2 ? cd/ft2 ?
candela per square inch cd/in2 ? cd/in2 ?
candela per square metre (SI unit); nit (deprecated[18]) cd/m2 ? cd/m2 = 1 cd/m2
footlambert fL ? (1/?) cd/ft2 ?
lambert L ? (104/?) cd/m2 ?
stilb (CGS unit) sb ? 104 cd/m2 = 104 cd/m2

Luminous flux

Luminous flux
Name of unit Symbol Definition Relation to SI units
lumen (SI unit) lm ? cd·sr = 1 lm = 1 cd·sr

Illuminance

Illuminance
Name of unit Symbol Definition Relation to SI units
footcandle; lumen per square foot fc ? lm/ft2 =
lumen per square inch lm/in2 ? lm/in2 ?
lux (SI unit) lx ? lm/m2 = 1 lx = 1 lm/m2
phot (CGS unit) ph ? lm/cm2 = 104 lx

Radiation - source activity

Radioactivity
Name of unit Symbol Definition Relation to SI units
becquerel (SI unit) Bq ? Number of disintegrations per second = 1 Bq = 1/s
curie Ci ? [43] =
rutherford (H) rd ? 1 MBq = 106 Bq

Although becquerel (Bq) and hertz (Hz) both ultimately refer to the same SI base unit (s-1), Hz is used only for periodic phenomena (ie repetitions at regular intervals), and Bq is only used for stochastic processes (ie at random intervals) associated with radioactivity.[44]

Radiation - exposure

Radiation - exposure
Name of unit Symbol Definition Relation to SI units
roentgen R 1 R ? [37] =

The roentgen is not an SI unit and the NIST strongly discourages its continued use.[45]

Radiation - absorbed dose

Radiation - absorbed dose
Name of unit Symbol Definition Relation to SI units
gray (SI unit) Gy ? 1 J/kg = 1 m2/s2[46] = 1 Gy
rad rad ? 0.01 Gy[37] = 0.01 Gy

Radiation - equivalent dose

Radiation - equivalent dose
Name of unit Symbol Definition Relation to SI units
Röntgen equivalent man rem ? 0.01 Sv = 0.01 Sv
sievert (SI unit) Sv ? 1 J/kg[44] = 1 Sv

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

H = Q · D

where H is the equivalent dose, D is the absorbed dose, and Q is a dimensionless quality factor. Thus, for any quantity of D measured in Gy, the numerical value for H measured in Sv may be different.[47]

See also

Notes and references

  1. ^ Béla Bodó; Colin Jones (26 June 2013). Introduction to Soil Mechanics. John Wiley & Sons. pp. 9-. ISBN 978-1-118-55388-6.
  2. ^ "Identity property of multiplication". Retrieved .
  3. ^ jobs (September 14, 2012). "The astronomical unit gets fixed : Nature News & Comment". Nature.com. doi:10.1038/nature.2012.11416. Retrieved 2013.
  4. ^ "NIST Reference on Constants, Units, and Uncertainty."(2010). National Institute of Standards and Technology. Retrieved October 17, 2014.
  5. ^ a b U.S. National Institute of Standards and Technology Handbook 44 Appendix C - General Tables of Units of Measurement 2013 Edition
  6. ^ a b c d e f g h i j k l m n Lide, D. (Ed.). (1990). Handbook of Chemistry and Physics (71st ed). Boca Raton, FL: CRC Press. Section 1.
  7. ^ a b 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.
  8. ^ The International Astronomical Union and Astronomical Units
  9. ^ Klein, Herbert Arthur. (1988). The Science of Measurement: a Historical Survey. Mineola, NY: Dover Publications 0-4862-5839-4.
  10. ^ a b c d e f The International System of Units, Section 2.1 (8 ed.), Bureau International des Poids et Mesures, 2006, archived from the original on October 1, 2009, retrieved 2009
  11. ^ International System of Units, Archived August 21, 2008, at the Wayback Machine. 8th ed. (2006), Bureau International des Poids et Mesures, Section 4.1 Table 8.
  12. ^ Cox, Arthur N., ed. (2000). Allen's Astrophysical Quantities (4th ed.). New York: AIP Press / Springer. Bibcode:2000asqu.book.....C. ISBN 0387987460.
  13. ^ Binney, James; Tremaine, Scott (2008). Galactic Dynamics (2nd ed.). Princeton, NJ: Princeton University Press. Bibcode:2008gady.book.....B. ISBN 978-0-691-13026-2.
  14. ^ P. Kenneth Seidelmann, Ed. (1992). Explanatory Supplement to the Astronomical Almanac. Sausalito, CA: University Science Books. p. 716 and s.v. parsec in Glossary.
  15. ^ a b c Whitelaw, Ian. (2007). A Measure of All Things: The Story of Man and Measurement. New York: Macmillan 0-312-37026-1. p. 152.
  16. ^ a b 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 2nd ed. New York: The Century Co. p. 142–150.
  17. ^ Pasko, Wesley Washington (1894). American dictionary of printing and bookmaking. (1894). New York: Howard Lockwood. p. 521.
  18. ^ a b c d e f g h Rowlett, Russ (2005), How Many? A Dictionary of Units of Measurement
  19. ^ Thompson, A. and Taylor, B.N. (2008). Guide for the Use of the International System of Units (SI). National Institute of Standards and Technology Special Publication 811. p. 57.
  20. ^ a b c d e US Code of Federal Regulations, Title 21, Section 101.9, Paragraph (b)(5)(viii), archived from the original on August 13, 2009, retrieved 2009
  21. ^ Barry N. Taylor, Ed.,NIST Special Publication 330: The International System of Units (SI) (2001 Edition), Washington: US Government Printing Office, 43,"The 12th Conference Generale des Poids et Mesures (CGPM)...declares that the word "litre" may be employed as a special name for the cubic decimetre".
  22. ^ a b [1]
  23. ^ CODATA Value: atomic unit of mass. (2010). National Institute of Standards and Technology. Retrieved 29 May 2015.
  24. ^ http://physics.nist.gov/cgi-bin/cuu/Value?tevj%7Csearch_for=electronvolt
  25. ^ The Swiss Federal Office for Metrology gives Zentner on a German language web page "Archived copy". Archived from the original on 2006-09-28. Retrieved . and quintal on the English translation of that page "Archived copy". Archived from the original on 2001-03-09. Retrieved .; the unit is marked "spécifiquement suisse !"
  26. ^ a b Pedersen O. (1983). "Glossary" in Coyne, G., Hoskin, M., and Pedersen, O. Gregorian Reform of the Calendar: Proceedings of the Vatican Conference to Commemorate its 400th Anniversary. Vatican Observatory. Available from Astrophysics Data System.
  27. ^ Richards, E.G. (1998), Mapping Time, Oxford University Press, pp. 94-95, ISBN 0-19-850413-6
  28. ^ Steel, Duncan (2000), Marking Time, John Wiley & Sons, p. 46, ISBN 0-471-29827-1
  29. ^ "CODATA Value: Planck time". physics.nist.gov. Retrieved .
  30. ^ a b Richards, E. G. (2013). "Calendars" in S. E. Urban & P. K. Seidelmann, eds. Explanatory Supplement to the Astronomical Almanac. Mill Valley, CA: University Science Books.
  31. ^ Richards, E. G. (2013). "Calendars" in S. E. Urban & P. K. Seidelmann, eds. Explanatory Supplement to the Astronomical Almanac. Mill Valley, CA: University Science Books. p. 587.
  32. ^ Tom Benson. (2010.) "Mach Number" in Beginner's Guide to Aeronautics. NASA.
  33. ^ CODATA Value: atomic unit of force. (2006). National Institute of Standards and Technology. Retrieved September 14, 2008.
  34. ^ a b c d e f g h i Comité International des Poids et Mesures, Resolution 2, 1946, retrieved 2009
  35. ^ a b c d e f g h i j k l m n o p 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, pp. 57–68.
  36. ^ 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.
  37. ^ a b c d e f g NIST Guide to SI Units, Appendix B.9, retrieved 2009
  38. ^ International System of Units, Archived July 16, 2012, at the Wayback Machine. 8th ed. (2006), Bureau International des Poids et Mesures, Section 4.1 Table 7.
  39. ^ The NIST Reference on Constants, Units, and Uncertainty, 2006, retrieved 2009
  40. ^ Robert G. Mortimer Physical chemistry,Academic Press, 2000 ISBN 0-12-508345-9, page 677
  41. ^ Standard for the Use of the International System of Units (SI): The Modern Metric System IEEE/ASTM SI 10-1997. (1997). New York and West Conshohocken, PA: Institute of Electrical and Electronics Engineers and American Society for Testing and Materials. Tables A.1 through A.5.
  42. ^ The NIST Reference on Constants, Units, and Uncertainty, retrieved 2009
  43. ^ Ambler Thompson & Barry N. Taylor. (2008). Guide for the Use of the International System of Units (SI). Special Publication 811. Gaithersburg, MD: National Institute of Standards and Technology. p. 10.
  44. ^ a b The International System of Units, Section 2.2.2., Table 3 (8 ed.), Bureau International des Poids et Mesures, 2006, archived from the original on June 18, 2007, retrieved 2009
  45. ^ The NIST Guide to the SI (Special Publication 811), section 5.2, 2008, retrieved 2009
  46. ^ Ambler Thompson & Barry N. Taylor. (2008). Guide for the Use of the International System of Units (SI). Special Publication 811. Gaithersburg, MD: National Institute of Standards and Technology. p. 5.
  47. ^ Comité international des poids et mesures, 2002, Recommendation 2, retrieved 2009
Notes
  1. ^ The technical definition of tropical year is the period of time for the ecliptic longitude of the Sun to increase 360 degrees. (Urban & Seidelmann 2013, Glossary, s.v. year, tropical)

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