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 |  |
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° = (  /180) rad |
geometric angle |
| minute |  |
1 = (1/60)° = ( /10 800) rad |
geometric angle |
| second |   |
1  = (1/60) = ( /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 |
km - kilometer, m - meter, dm - decimeter, cm - centimeter, mm - millimeter