# Engineering Statics/Appendices/SI Units Used in Mechanics
## SI Units Used in Mechanics

| Quantity | Unit | SI Symbol |
| (Base Units) | | |
| Length | meter* | m |
| Mass | kilogram | kg |
| Time | second | s |
| (Derived Units) | | |
| Acceleration, linear | meter/second$^2$ | m/s$^2$ |
| Acceleration, angular | radian/second$^2$ | rad/s$^2$ |
| Area | meter$^2$ | m$^2$ |
| Density | kilogram/meter$^3$ | kg/m$^3$ |
| Force | newton | N (= kg-m/s$^2$) |
| Frequency | hertz | Hz (= 1/s) |
| Impulse, linear | newton-second | N-s |
| Impulse, angular | newton-meter-second | N-m-s |
| Moment of force | newton-meter | N-m |
| Moment of inertia, area | meter$^4$ | m$^4$ |
| Moment of inertia, mass | kilogram-meter$^2$ | kg-m$^2$ |
| Momentum, linear | kilogram-meter/second | kg-m/s (= N-s) |
| Moment, angular | kilogram-meter$^2$/second | kg-m$^2$/s (= N-m-s) |
| Power | watt | W (= J/s = N-m/s) |
| Pressure, stress | pascal | Pa (= N/m$^2$) |
| Product of inertia, area | meter$^4$ | m$^4$ |
| Product of inertia, mass | kilogram-meter$^2$ | kg-m$^2$ |
| Spring constant | newton/meter | N/m |
| Velocity, linear | meter/second | m/s |
| Velocity, angular | radian/second | rad/s |
| Volume | meter$^3$ | m$^3$ |
| Work, energy | joule | J (= N-m) |
| (Supplementary and Other Acceptable Units) | (Supplementary and Other Acceptable Units) | |
| Distance (navigation) | nautical mile | (= 1,852 km) |
| Mass | ton (metric) | t (= 1,000 kg) |
| Plane angle | degrees (decimal) | ° |
| Plane angle | radian | — |
| Speed | knot | (1.852 km/h) |
| Time | day | d |
| Time | hour | h |
| Time | minute | min |
| * Also spelled metre | * Also spelled metre | |
Metric prefixes :
| Prefix | Symbol | 1000$^m$ | 10$^n$ | Decimal | Short scale | Long scale | Since |
| yotta | Y | 1000$^8$ | 10$^{24}$ | 1,000,000,000,000,000,000,000,000 | Septillion | Quadrillion | 1991 |
| zetta | Z | 1000$^7$ | 10$^{21}$ | 1,000,000,000,000,000,000,000 | Sextillion | Trilliard | 1991 |
| exa | E | 1000$^6$ | 10$^{18}$ | 1,000,000,000,000,000,000 | Quintillion | Trillion | 1975 |
| peta | P | 1000$^5$ | 10$^{15}$ | 1,000,000,000,000,000 | Quadrillion | Billiard | 1975 |
| tera | T | 1000$^4$ | 10$^{12}$ | 1,000,000,000,000 | Trillion | Billion | 1960 |
| giga | G | 1000$^3$ | 10$^9$ | 1,000,000,000 | Billion | Milliard | 1960 |
| mega | M | 1000$^2$ | 10$^6$ | 1,000,000 | Million | Million | 1960 |
| kilo | k | 1000$^1$ | 10$^3$ | 1000 | Thousand | Thousand | 1795 |
| hecto | h | 1000$^{2/3}$ | 10$^2$ | 100 | Hundred | Hundred | 1795 |
| deca | da | 1000$^{1/3}$ | 10$^1$ | 10 | Ten | Ten | 1795 |
| | | 1000$^0$ | 10$^0$ | 1 | One | One | – |
| deci | d | 1000$^{−1/3}$ | 10$^{−1}$ | 0.1 | Tenth | Tenth | 1795 |
| centi | c | 1000$^{−2/3}$ | 10$^{−2}$ | 0.01 | Hundredth | Hundredth | 1795 |
| milli | m | 1000$^{−1}$ | 10$^{−3}$ | 0.001 | Thousandth | Thousandth | 1795 |
| micro | μ | 1000$^{−2}$ | 10$^{−6}$ | 0.000001 | Millionth | Millionth | 1960 |
| nano | n | 1000$^{−3}$ | 10$^{−9}$ | 0.000000001 | Billionth | Milliardth | 1960 |
| pico | p | 1000$^{−4}$ | 10$^{−12}$ | {0.000000000001 | Trillionth | Billionth | 1960 |
| femto | f | 1000$^{−5}$ | 10$^{−15}$ | 0.000000000000001 | Quadrillionth | Billiardth | 1964 |
| atto | a | 1000$^{−6}$ | 10$^{−18}$ | 0.000000000000000001 | Quintillionth | Trillionth | 1964 |
| zepto | z | 1000$^{−7}$ | 10$^{−21}$ | 0.000000000000000000001 | Sextillionth | Trilliardth | 1991 |
| yocto | y | 1000$^{−8}$ | 10$^{−24}$ | 0.000000000000000000000001 | Septillionth | Quadrillionth | 1991 |
| ↑ The metric system was introduced in 1795 with six prefixes. The other dates relate to recognition by a resolution of the CGPM. ||||||||

### Selected Rules for Writing Metric Quantities

* For readability, use unit prefixes such that the number is between 0.1 and 1000.
* The most common prefixes in engineering are giga, mega, kilo, centi, milli, and micro. Prefixes like hecto, deka, and deci make for awkward numbers.
* Unit combinations should only use prefixes in the numerator (write kJ/s instead of J/ms), with the exception of kg.
* Do not double up the prefixes, e.g. write GW not kMW.
* Use a dot to multiply units (write N•m not Nm)
* Avoid the ambiguity of multiple divisions (write N/m$^3$ not N/m/m/m)
* Exponents refer to the entire unit symbol (mm$^2$ means (mm)$^2$)
* Use spaces instead of commas to make long numbers easier to read (e.g. 1 210 000 000.001 W), ignore for numbers of four digits.