What SI is
The International System of Units, abbreviated SI, is the modern metric system used in science and most engineering around the world. It defines a small set of base units, from which all other units are built, and a set of prefixes that scale them by powers of ten. Some industries and countries still use other units alongside it, so you will often need to convert; a clear method for unit conversion is covered separately.
The seven base units
| Quantity | Unit | Symbol |
|---|---|---|
| Length | metre | m |
| Mass | kilogram | kg |
| Time | second | s |
| Electric current | ampere | A |
| Thermodynamic temperature | kelvin | K |
| Amount of substance | mole | mol |
| Luminous intensity | candela | cd |
The kilogram is the odd one out: it is a base unit that already contains a prefix, so prefixes for mass are applied to the gram (a milligram is one millionth of a kilogram, not one thousandth of one).
Common derived units
Derived units are combinations of base units. Some have their own names.
- Newton (N): force. 1 N = 1 kg·m/s².
- Pascal (Pa): pressure. 1 Pa = 1 N/m².
- Joule (J): energy. 1 J = 1 N·m = 1 kg·m²/s².
- Watt (W): power. 1 W = 1 J/s.
- Hertz (Hz): frequency. 1 Hz = 1 cycle per second, or 1/s.
- Volt (V), ohm (Ω), farad (F): electrical potential, resistance and capacitance.
When you check a formula using dimensional analysis, you expand these into base units to see whether both sides match.
Prefixes from nano to giga
| Prefix | Symbol | Factor |
|---|---|---|
| nano | n | 10^-9 |
| micro | µ | 10^-6 |
| milli | m | 10^-3 |
| (none) | 1 | |
| kilo | k | 10^3 |
| mega | M | 10^6 |
| giga | G | 10^9 |
Others exist, including pico (10^-12), centi (10^-2) and tera (10^12). Centi is common for centimetres but rarely used for other quantities in engineering work. The use of exponents here ties in with scientific notation: engineering notation uses exactly these steps of three.
Case matters
The capitalisation of symbols is part of the system.
- m is milli or metre; M is mega. 5 mW is five milliwatts; 5 MW is five megawatts. They differ by a factor of a billion.
- k is lowercase for kilo; K is kelvin.
- µ (the Greek letter mu) is micro. Where it cannot be typed, “u” is often used informally, so check the context.
- Pa, N, W and other units named after people are capitalised, but the full names (newton, watt) are written in lowercase.
A misread prefix on a datasheet or drawing can be a serious error. When reading datasheets, take a moment to confirm each prefix and its unit, especially where text is small.
Conversion practice
Use the factors from the table and write out the steps. Every answer below was checked by hand.
- 2.2 kΩ in ohms. 2.2 × 1,000 = 2,200 Ω.
- 0.5 A in milliamperes. 0.5 × 1,000 = 500 mA.
- 250 mV in volts. 250 × 10^-3 = 0.25 V.
- 4,700 µF in millifarads. 4,700 × 10^-6 F = 4.7 × 10^-3 F = 4.7 mF.
- 150 nm in micrometres. 150 × 10^-9 m = 0.15 × 10^-6 m = 0.15 µm.
- 3.3 GHz in hertz. 3.3 × 10^9 Hz = 3,300,000,000 Hz.
- 2.5 MΩ in kilohms. 2.5 × 10^6 Ω ÷ 10^3 = 2,500 kΩ.
- 47 nF in microfarads. 47 × 10^-9 F = 0.047 × 10^-6 F = 0.047 µF.
Notice that to move between two prefixes, you only need the difference in their exponents. From milli to micro is a step of three powers of ten, a factor of a thousand.
Squares and cubes
Prefixes apply to the unit as a whole, including powers. 1 mm² means (1 mm)², which is (10^-3 m)² = 10^-6 m², not 10^-3 m². Likewise 1 cm³ = (10^-2 m)³ = 10^-6 m³, which equals 1 mL. Forgetting to square the factor is one of the most common mistakes in area and volume conversions.
Units outside SI that you will meet
Some units are accepted for use alongside SI, such as the litre, the minute and hour, and the degree Celsius. Others, including inches, pounds and psi, belong to other systems. Dimensions on a supplier’s package drawings may be given in one, with a converted value in brackets. Treat the stated units, not your assumption, as the authority.
Computing has its own wrinkles: kilobyte and kibibyte, for example, are not the same, and storage and memory quantities are sometimes stated with different conventions. When it matters, check which one a source uses.
Habits that prevent mistakes
- Always write the unit with the number.
- Put values in scientific or engineering notation before multiplying.
- Make a quick plausibility check: a 100 µF capacitor is not a 100 F capacitor, and a result of that size should prompt a double-check, as in sanity checks.
- Use standard symbols and avoid inventing abbreviations in reports and procedures.
Standards and conventions for unit use differ between industries and countries, so follow the ones set for your own work.