Section 1 of 5The SI Base Units
The International System of Units uses a small set of base units from which every other unit is built.
Mass
- The kilogram, kg, is the SI base unit of mass, and is the one base unit that includes a prefix.
Length
- The metre, m, is the base unit of length or distance.
Time
- The second, s, is the base unit of time.
Current
- The ampere, A, is the base unit of electric current.
Temperature and amount
- The kelvin, K, measures thermodynamic temperature and the mole, mol, measures amount of substance.
Section 2 of 5Derived Units
Derived Units
Newton
- N = kg m s⁻², from force equals mass times acceleration.
Joule
- J = N m = kg m² s⁻², from work done equals force times distance.
Watt
- W = J s⁻¹ = kg m² s⁻³, from power equals energy divided by time.
Pascal
- Pa = N m⁻² = kg m⁻¹ s⁻², from pressure equals force divided by area.
Coulomb
- C = A s, because charge equals current multiplied by time.
| Unit | Name | In base units |
|---|---|---|
| N | newton | kg m s⁻² |
| J | joule | kg m² s⁻² |
| W | watt | kg m² s⁻³ |
| V | volt | kg m² s⁻³ A⁻¹ |
| Ω | ohm | kg m² s⁻³ A⁻² |
Section 3 of 5Finding a Unit
1
Write the defining equation for the quantity, such as pressure = force ÷ area.
2
Replace each quantity by its unit, so pressure becomes N ÷ m².
3
Replace any derived unit by its base units: N becomes kg m s⁻².
4
Simplify by combining powers of the same unit, giving kg m s⁻² ÷ m² = kg m⁻¹ s⁻².
5
Write the unit with negative powers rather than division signs, which keeps the result unambiguous.
Section 4 of 5Worked Example
Question Show that the unit of potential difference, the volt, can be written as kg m² s⁻³ A⁻¹.
- Potential difference = power ÷ current, so V = W ÷ A.
- The watt in base units is kg m² s⁻³.
- Dividing by the ampere gives kg m² s⁻³ A⁻¹.
Answer 1 V = 1 kg m² s⁻³ A⁻¹.
Section 5 of 5Exam Checklist & Tips
2.1.2 – Key Points for the Exam
- SI unit A unit belonging to the International System of Units, the agreed standard for science.
- Base unit One of the fundamental SI units from which all other units are derived.
- Derived unit A unit made by combining base units, such as the newton.
- Kelvin The SI base unit of thermodynamic temperature.
- Mole The SI base unit for the amount of substance.
Common Mistakes
- Using the gram as the SI base unit of mass instead of the kilogram.
- Writing the unit of charge as C = A/s instead of A s.
- Forgetting that temperature in kelvin does not use the degree symbol.
- Using the same letter for a quantity and its unit, such as writing the unit of mass as m.