Last reviewed 30 Sept 2026 · 9 min read
Measurement and units
Physics is a science of measurement. To measure a quantity means to compare it with an agreed standard of the same kind, called a unit. A result is always written as a number and a unit: length = 5 m.
A quantity that can be measured is a physical quantity — length, mass, time, force, temperature. Quantities like beauty or honesty cannot be measured and are not physical quantities.
- Fundamental (base) quantities are independent of one another: length, mass, time, electric current, temperature, amount of substance, luminous intensity.
- Derived quantities are combinations of base quantities: area, volume, speed, force, energy.
The SI system
The International System of Units (SI) is the modern metric system used all over the world. It has seven base units:
| Quantity | SI 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 |
Two supplementary (dimensionless) angle units are the radian (plane angle) and the steradian (solid angle).
Since 2019 the SI units are defined by fixing the values of natural constants (for example the speed of light, Planck's constant and the Boltzmann constant). The kilogram is defined through Planck's constant, the second through the caesium-133 atomic transition frequency, and the metre through the distance light travels in a fixed fraction of a second (light travels 299,792,458 m in one second).
Metre, Kilogram, Second, Ampere, Kelvin, Mole, Candela — length, mass, time, current, temperature, amount, light intensity.
Other systems
- CGS: centimetre, gram, second.
- FPS: foot, pound, second (British).
- MKS: metre, kilogram, second — the basis of SI.
Derived units
| Quantity | Formula | SI unit | Symbol / equivalent |
|---|---|---|---|
| Area | length × breadth | square metre | m² |
| Volume | length³ | cubic metre | m³ |
| Speed / velocity | distance / time | metre per second | m/s |
| Acceleration | velocity / time | metre per second² | m/s² |
| Density | mass / volume | kilogram per cubic metre | kg/m³ |
| Force | mass × acceleration | newton | N = kg·m/s² |
| Pressure | force / area | pascal | Pa = N/m² |
| Work, energy, heat | force × distance | joule | J = N·m |
| Power | work / time | watt | W = J/s |
| Frequency | 1 / time period | hertz | Hz = s⁻¹ |
| Electric charge | current × time | coulomb | C = A·s |
| Potential difference | work / charge | volt | V = J/C |
| Resistance | V / I | ohm | Ω = V/A |
| Capacitance | charge / voltage | farad | F = C/V |
| Magnetic flux | weber | Wb | |
| Magnetic flux density | tesla | T = Wb/m² | |
| Inductance | henry | H | |
| Radioactivity | becquerel | Bq = decays/s | |
| Absorbed dose | gray | Gy = J/kg | |
| Luminous flux | lumen | lm | |
| Illuminance | lux | lx = lm/m² |
Special and practical units
| Unit | Use | Value |
|---|---|---|
| Light year | astronomical distance | about 9.46 × 10¹⁵ m |
| Astronomical unit (AU) | distance in the solar system | about 1.496 × 10¹¹ m (mean Earth–Sun distance) |
| Parsec | astronomical distance | about 3.26 light years |
| Angstrom (Å) | atomic dimensions | 10⁻¹⁰ m |
| Fermi (femtometre) | nuclear dimensions | 10⁻¹⁵ m |
| Micron (micrometre) | small lengths | 10⁻⁶ m |
| Quintal | mass | 100 kg |
| Tonne (metric ton) | mass | 1000 kg |
| Atomic mass unit (u) | atomic masses | about 1.66 × 10⁻²⁷ kg |
| Electron volt (eV) | atomic energy | about 1.6 × 10⁻¹⁹ J |
| Horsepower (hp) | engine power | about 746 W |
| Calorie | heat | about 4.18 J |
| Bar | pressure | 10⁵ Pa (about one atmosphere) |
| Atmosphere (atm) | pressure | about 1.013 × 10⁵ Pa |
| Torr / mm Hg | pressure | about 133 Pa |
| Knot | speed of ships | about 1.852 km/h |
| Nautical mile | sea distance | 1852 m |
| Kilowatt-hour (kWh) | electrical energy ("unit" of electricity) | 3.6 × 10⁶ J |
| Mach number | speed relative to sound | ratio; Mach 1 ≈ speed of sound |
| Decibel (dB) | sound intensity level | logarithmic |
SI prefixes
| Prefix | Symbol | Factor |
|---|---|---|
| tera | T | 10¹² |
| giga | G | 10⁹ |
| mega | M | 10⁶ |
| kilo | k | 10³ |
| hecto | h | 10² |
| deca | da | 10 |
| deci | d | 10⁻¹ |
| centi | c | 10⁻² |
| milli | m | 10⁻³ |
| micro | µ | 10⁻⁶ |
| nano | n | 10⁻⁹ |
| pico | p | 10⁻¹² |
| femto | f | 10⁻¹⁵ |
Dimensions
The dimensions of a physical quantity show how it is made up of the base quantities mass [M], length [L] and time [T] (and others). For example:
| Quantity | Dimensional formula |
|---|---|
| Area | |
| Volume | |
| Velocity | |
| Acceleration | |
| Force | |
| Work / energy | |
| Power | |
| Pressure | |
| Density | |
| Frequency | |
| Momentum |
Uses of dimensions: to check whether a formula is dimensionally correct (both sides must have the same dimensions), to convert units, and to derive the form of a relation. Dimensional analysis cannot give numerical constants (such as ½ or 2π) and cannot handle sums of functions such as sine.
Quantities with the same dimensions as each other: work, energy and torque all have ; pressure, stress and energy density have ; strain, angle and refractive index are dimensionless.
Is the equation dimensionally correct?
Solution. ; ; . All terms have the dimension , so the equation is dimensionally correct.