International System of Units (SI)

The Metric System


SI Base Units

Base Unit Symbol  
meter m length
kilogram kg mass
second s time
ampere A electric current
kelvin K thermodynamic temperature
mole mol amount of substance
candela cd luminous intensity

SI Derived Units

Derived Unit Symbol  
square meter m2 area
cubic meter m3 volume
meter per second m/s speed, velocity
meter per second squared m/s2 acceleration
reciprocal meter m-1 wave number
kilogram per cubic meter kg/m3 mass density
cubic meter per kilogram m3/kg specific volume
ampere per square meter A/m2 current density
ampere per meter A/m magnetic field strength
mole per cubic meter mol/m3 amount-of-substance concentration
candela per square meter cd/m2 luminance
kilogram per kilogram kg/kg mass fraction

SI Derived Units – with special names

Name Symbol Other SI units equivalent SI base units equivalent  
radian rad   m·m-1 plane angle
steradian sr   m2·m-2 solid angle
hertz Hz   s-1 frequency
newton N   m·kg·s-2 force
pascal Pa N/m2 m-1·kg·s-2 pressure, stress
joule J N·m m2·kg·s-2 energy, work, quantity of heat
watt W J/s m2·kg·s-3 power, radiant flux
coulomb C   s·A electric charge, quantity of electricity
volt V W/A m2·kg·s-3·A-1 electric potential difference, electromotive force
farad F C/V m-2·kg-1·s4·A2 capacitance
ohm Omega V/A m2·kg·s3·A-2 electric resistance
siemens S A/V m-2·kg-1·s3·A2 electric conductance
weber Wb V·s m2·kg·s-2·A-1 magnetic flux
tesla T Wb/m2 kg·s-2·A-1 magnetic flux density
henry H Wb/A m2·kg·s-2·A-2 inductance
Celsius °C   K Celsius temperature
lumen lm cd·sr m2·m-22·cd = cd luminous flux
lux lx lm/m2 m2·m-4·cd = m-2·cd illuminance
becquerel Bq   s-1 activity (of a radionuclide)
gray Gy J/kg m2·s-2 absorbed dose, specific energy (imparted), kerma
sievert Sv J/kg m2·s-2 dose equivalent
katal kat   s-1·mol catalytic activity

Units outside the SI

NOTE: These are NOT SI units. However, they are acceptable for use within SI.

Name Symbol Value in SI units  
minute min 1 min = 60 s time
hour h 1 h = 60 min = 3600 s time
day d 1 d = 24 h = 86 400 s time
degree ° 1° = ( pi/180) rad geometric angle
minute ' 1' = (1/60)° = (pi/10 800) rad geometric angle
second '' 1'' = (1/60)' = (pi/648 000) rad geometric angle
liter l or L 1 L = 1 dm3 = 10-3 m3 volume
metric ton t 1 t = 103 kg mass
neper Np 1 Np = 1 logarithmic unit
bel B 1 B = (1/2) ln 10 Np intensity of sound
electronvolt eV 1 eV = 1.602 18 x 10-19 J, approx. energy unit
atomic mass unit u 1 u = 1.660 54 x 10-27 kg, approx. mass
astronomical unit ua or AU 1 ua = 1.495 98 x 1011 m, approx. length
nautical mile   1 nautical mile = 1852 m nautical length
knot   1 nautical mile per hour = (1852/3600) m/s nautical speed
are a 1 a = 1 dam2 = 102 m2 area
hectare  ha 1 ha = 1 hm2 = 104 m2 area
bar bar 1 bar = 0.1 MPa = 100 kPa = 1000 hPa = 105 Pa pressure
ångström Å 1 Å = 0.1 nm = 10-10 m length
barn b 1 b = 100 fm2 = 10-28 m2 area
curie Ci 1 Ci = 3.7 x 1010 Bq radioactivity
roentgen R 1 R = 2.58 x 10-4 C/kg ionizing radiation
rad rad 1 rad = 1 cGy = 10-2 Gy absorbed radiation dose
rem rem 1 rem = 1 cSv = 10-2 Sv radiation dosage applied

Prefixes

Commonly recognized prefixes and their meaning used with SI units.

Prefix   Value Value Cardinal Name
yotta, (Y) = 1,000,000,000,000,000,000,000,000 1024 septillion
zetta, (Z) = 1,000,000,000,000,000,000,000 1021 sextillion
exa, (E) = 1,000,000,000,000,000,000 1018 quintillion
peta, (P) = 1,000,000,000,000,000 1015 quadrillion
tera, (T) = 1,000,000,000,000 1012 trillion
giga, (G) = 1,000,000,000 109 billion
mega, (M) = 1,000,000 106 million
kilo, (k) = 1,000 103 thousand
hecto, (h) = 100 102 hundred
deka, (da) = 10 101 ten
         
deci, (d) = 0.1 10-1 tenth
centi, (c) = 0.01 10-2 hundredth
milli, (m) = 0.001 10-3 thousandth
 micro, (µ) = 0.000001 10-6 millionth
nano, (n) = 0.000000001 10-9 billionth
pico, (p) = 0.000000000001 10-12 trillionth
femto, (f) = 0.000000000000001 10-15 quadrillionth
atto, (a) = 0.000000000000000001 10-18 quintillionth
 zepto, (z) = 0.000000000000000000001 10-21 sextillionth
yocto, (y) = 0.000000000000000000000001 10-24 septillionth

Units of Length

1 centimeter (cm) = 10 millimeters (mm)
1 decimeter (dm) = 10 centimeters = 100 millimeters
1 meter (m) = 10 decimeters = 1000 millimeters
1 dekameter (dam) = 10 meters
1 hectometer (hm) = 10 dekameters = 100 meters
1 kilometer (km) = 10 hectometers = 1000 meters

Units of Area

1 square centimeter (cm2) = 100 square millimeters (mm2)
1 square decimeter (dm2) = 100 square centimeters
1 square meter (m2) = 100 square decimeters
1 are = 100 square meters = 1 square dekameter (dam2)
1 hectare (ha) = 100 square dekameters = 1 square hectometer (hm2)
1 square kilometer (km2) = 100 square hectometers

Units of Liquid Volume

1 liter = 1 cubic decimeter.
1 centiliter (cL) = 10 milliliters (mL)
1 deciliter (dL) = 10 centiliters = 100 milliliters
1 liter = 10 deciliters = 1000 milliliters
1 dekaliter (daL) = 10 liters =
1 hectoliter (hL) = 10 dekaliters = 100 liters
1 kiloliter (kL) = 10 hectoliters = 1000 liters

Units of Volume

1 cubic centimeter (cm3) = 1000 cubic millimeters (mm3)
1 cubic decimeter (dm3) = 1000 cubic centimeters = 1,000,000 cubic millimeters
1 cubic meter (m3) = 1,000,000 cubic centimeters = 1,000,000,000 cubic millimeters

Units of Mass

1 gram (g) = 10 decigrams = 1000 milligrams
1 centigram (cg) = 10 milligrams (mg)
1 decigram (dg) = 10 centigrams = 100 milligrams
1 dekagram (dag) = 10 grams
1 hectogram (hg) = 10 dekagrams = 100 grams
1 kilogram (kg) = 10 hectograms = 1000 grams
1 megagram (Mg) = 1 metric ton(t) = 1000 kilograms

United States Units of Measure (English System)

NOTE: English units of measure are NOT part of the SI Units of measure.

Units of Length

1 foot (ft) = 12 inches (in)
1 yard (yd) = 3 feet
1 rod (rd), pole, or perch = 16-1/2 feet
1 furlong (fur) = 660 feet = 40 rods
1 U.S. statute mile (mi) = 5280 feet = 8 furlongs
1 international nautical mile = 6076.11549 feet (approximately) = 1852 meters

Units of Area

1 square foot (ft2) = 144 square inches (in2)
1 square yard (yd2) = 9 square feet = 1296 square inches
1 square rod (sq rd) = 2721/4 square feet
1 acre = 43 560 square feet = 160 square rods
1 square mile (mi2) = 640 acres = 1 section of land
1 township = 6 miles square
36 sections = 36 square miles

Units of Volume

1 cubic foot (ft3) = 1728 cubic inches (in3)
1 cubic yard (yd3) = 27 cubic feet
1 link (li) = 0.66 foot (ft)
1 chain (ch) = 100 links = 4 rods = 66 feet
1 U.S. statute mile (mi) = 5280 feet = 320 rods = 80 chains

Units of Liquid Volume

1 pint (pt) = 4 gills (gi) = 28.875 cubic inches = 16 fluid ounces
1 quart (qt) = 2 pints = 57.75 cubic inches
1 gallon (gal) = 4 quarts = 231 cubic inches = 8 pints = 32 gills

Units of Dry Volume

1 quart (qt) = 2 pints (pt) = 67.200 6 cubic inches
1 peck (pk) = 8 quarts = 537.605 cubic inches = 16 pints
1 bushel (bu) = 4 pecks = 2150.42 cubic inches = 32 quarts

Units of Weight

1 hundredweight (cwt) = 100 pounds
1 ton = 2000 pounds = 20 hundredweights

British Units of Measurement

1 stone = 14 pounds
1 ton = 2240 pounds = 20 hundredweight
1 quart = 2 pints
1 gallon = 4 quarts
1 bushel = 8 gallons (4 pecks)

Other Common Equivalents

1 acre = 43,560 ft2 = 0.0015625 mi2
1 liter = 0.908083 quarts = 0.2641721 gallons
1 gallon = 3.785412 liters
1 kilogram = 2.204623 pounds
1 pound = 0.45359237 kilograms
1 angstrom = 0.1 nanometer = 0.0001 micrometer = 0.0000001 millimeter = 0.000000004 inch.
1 fathom = 6 feet = 1.8288 meters.
1 league = 3 miles = 4.828 kilometers

Conversions of SI and English Units of Measurement

(all bold figures are exact)

Units Inches Feet Yards Miles Centimeters Meters
1 inch = 1 0.08333333 0.02777778 0.00001578283 2.54 0.0254
1 foot = 12 1 0.3333333 0.0001893939 30.48 0.3048
1 yard = 36 3 1 0.0005681818 91.44 0.9144
1 mile = 63,360 5,280 1,760 1 160,934.4 1,609.344
1 centimeter = 0.3937008 0.03280840 0.01093613 0.000006213712 1 0.01
1 meter = 39.37008 3.280840 1.093613 0.0006213712 100 1

Metric Conversion
km - kilometer, m - meter, dm - decimeter, cm - centimeter, mm - millimeter