SI Base Units and Metric Prefixes
The SI (International System of Units) is the modern metric system used in science worldwide, built on seven base units, and metric prefixes such as kilo-, milli- and micro- are used to write very large or very small quantities as multiples of powers of ten. In brief: the base units used most often in school physics are the meter (length), kilogram (mass), second (time), kelvin (temperature) and ampere (current). A prefix multiplies the unit: 1 km = 103 m and 1 mm = 10−3 m.
Measurement means comparing a quantity with an agreed standard unit. Having one international system lets scientists, engineers and traders share results without confusion. This guide describes the SI units for length, mass, time and temperature, explains how to choose a suitable unit, lists the metric prefixes in a table, works through conversions and corrects common mistakes.
What is measurement?
To measure a quantity is to find how many times a chosen unit fits into it. A measurement has a number, a unit and an uncertainty. A good unit is well defined, available to everyone and does not change. For this reason, modern units are defined from constants of nature rather than from objects.
What are the SI base units?
- Length – meter (m): defined as the distance light travels in a vacuum in 1/299,792,458 of a second.
- Mass – kilogram (kg): since 2019 defined by fixing the value of the Planck constant. Before that, it was the mass of a platinum-iridium cylinder kept near Paris. The kilogram is the only base unit with a prefix in its name. A gram is 10−3 kg.
- Time – second (s): defined from the frequency of radiation of the cesium-133 atom, which has 9,192,631,770 periods in one second.
- Temperature – kelvin (K): the unit of thermodynamic temperature. 0 K is absolute zero. A temperature interval of 1 K is equal to 1 °C, and T(K) = T(°C) + 273.15.
- Electric current – ampere (A), amount of substance – mole (mol) and luminous intensity – candela (cd) are the other base units.
All the other units are derived. For example, the newton is 1 kg·m/s2, and the joule is 1 N·m. Units that are not part of the SI but accepted for use are the minute, hour, day, liter (L, 1 L = 10−3 m3) and tonne (t = 1,000 kg).
How do you choose an appropriate unit?
Select a unit of a convenient size, so that the number is easy to read. A classroom is measured in meters, a coin in millimeters, the distance between cities in kilometers, and the wavelength of light in nanometers. A pill is measured in milligrams, a person in kilograms, and a ship in tonnes. For calculations in formulas, the base SI units (m, kg, s) are used, unless the formula states otherwise.
Metric prefixes
| Prefix | Symbol | Factor | Example |
|---|---|---|---|
| giga | G | 109 | 1 GHz = 109 Hz |
| mega | M | 106 | 1 MW = 106 W |
| kilo | k | 103 | 1 km = 1,000 m |
| centi | c | 10−2 | 1 cm = 0.01 m |
| milli | m | 10−3 | 1 mm = 0.001 m |
| micro | µ | 10−6 | 1 µm = 10−6 m |
| nano | n | 10−9 | 1 nm = 10−9 m |
Worked example: converting with prefixes
Convert 2.5 km to m, 350 mg to kg, 45 ms to s, and 3.2 GHz to Hz.
- 2.5 km: 2.5 × 103 m = 2,500 m.
- 350 mg: 350 × 10−3 g = 0.350 g. Then 0.350 g × 10−3 kg/g = 3.5 × 10−4 kg.
- 45 ms: 45 × 10−3 s = 0.045 s.
- 3.2 GHz: 3.2 × 109 Hz = 3,200,000,000 Hz.
For the reverse direction, divide by the factor: 0.045 s ÷ 10−3 = 45 ms. A useful check is that the number gets bigger when you use a smaller unit (2,500 m is a bigger number than 2.5 km, but the same length).
How was the metric system developed?
The metric system was introduced in France in the 1790s, with the meter defined as one ten-millionth of the distance from the North Pole to the equator along the meridian through Paris. The Metre Convention of 1875 created international standards, and the SI was established in 1960. In 2019 all base units were redefined using fixed values of constants such as the speed of light and the Planck constant. Only a few countries, including the United States, Liberia and Myanmar, do not use metric units as their main system for everyday life.
Which mistakes are common?
Mistake 1: Confusing milli and mega
Lowercase m means milli (10−3), and capital M means mega (106). The difference is a factor of 109.
Mistake 2: Treating the gram as the base unit of mass
The SI base unit is the kilogram, so conversions to kg are needed before using formulas.
Mistake 3: Using °C in formulas that need kelvins
Gas laws and many thermal formulas require absolute temperature in kelvins.
Mistake 4: Squaring the prefix incorrectly
1 cm2 is (0.01 m)2 = 10−4 m2, not 10−2 m2.