SI Units and Prefixes

This lesson covers the International System of Units (SI) and how to use unit prefixes and standard form — as required by the Edexcel GCSE Physics specification (1PH0), Topic 1: Key Concepts of Physics. You need to know the SI base units, common derived units, unit prefixes, and how to convert between them confidently.

The SI Base Units

The SI system is the internationally agreed system of measurement used in science. There are seven base units from which all other units are derived. At GCSE level you need to be aware of these and use several of them regularly.

Quantity	SI Base Unit	Symbol
Length	metre	m
Mass	kilogram	kg
Time	second	s
Electric current	ampere	A
Temperature	kelvin	K
Amount of substance	mole	mol
Luminous intensity	candela	cd

Key Points

The kilogram (kg) is the SI unit of mass — not the gram. This is unusual because it already contains a prefix (kilo).
The second (s) is the SI unit of time — not the minute or hour.
The kelvin (K) is the SI unit of temperature — not degrees Celsius. However, at GCSE you will often use degrees Celsius (°C) in practice. To convert: K = °C + 273.

Exam Tip: You do not need to memorise all seven base units for the Edexcel GCSE exam, but you must be comfortable using metres, kilograms, seconds, amperes and kelvins in calculations.

Derived Units

Derived units are combinations of base units used to measure other physical quantities. You will encounter these throughout your GCSE Physics course.

Quantity	Derived Unit	Symbol	In Base Units
Force	newton	N	kg m/s²
Energy	joule	J	kg m²/s²
Power	watt	W	kg m²/s³ (= J/s)
Pressure	pascal	Pa	kg/(m s²) (= N/m²)
Frequency	hertz	Hz	1/s (= s⁻¹)
Charge	coulomb	C	A s
Potential difference	volt	V	kg m²/(A s³) (= J/C)
Resistance	ohm	Ω	kg m²/(A² s³) (= V/A)

Understanding Derived Units

Each derived unit can be broken down into base units. For example:

1 newton (N) is the force needed to accelerate a mass of 1 kg at 1 m/s². So 1 N = 1 kg m/s².
1 joule (J) is the energy transferred when a force of 1 N moves an object 1 m. So 1 J = 1 N m = 1 kg m²/s².
1 watt (W) is the rate of energy transfer of 1 joule per second. So 1 W = 1 J/s.

Exam Tip: You are not required to derive these units from scratch in the exam, but you must know what each unit measures and be able to use the correct unit in your answers. Losing a mark for an incorrect or missing unit is one of the most common errors.

Unit Prefixes

Prefixes are placed before a unit to indicate a multiple or fraction of that unit. You must know the following prefixes and be able to convert between them.

Prefix	Symbol	Multiplier	Example
nano	n	10⁻⁹ (0.000 000 001)	1 nm = 1 × 10⁻⁹ m
micro	μ	10⁻⁶ (0.000 001)	1 μs = 1 × 10⁻⁶ s
milli	m	10⁻³ (0.001)	1 mm = 1 × 10⁻³ m
centi	c	10⁻² (0.01)	1 cm = 1 × 10⁻² m
kilo	k	10³ (1 000)	1 km = 1 × 10³ m
mega	M	10⁶ (1 000 000)	1 MHz = 1 × 10⁶ Hz
giga	G	10⁹ (1 000 000 000)	1 GW = 1 × 10⁹ W

Converting Between Units

When performing physics calculations, you must convert all values to SI base units before substituting into an equation. Here is how to convert:

Converting to Larger or Smaller Units

To convert from a smaller unit to a larger unit, divide.
To convert from a larger unit to a smaller unit, multiply.

Worked Examples

Example 1: Convert 4.5 km to metres.

1 km = 1000 m
4.5 km = 4.5 × 1000 = 4500 m

Example 2: Convert 250 g to kilograms.

1 kg = 1000 g
250 g = 250 ÷ 1000 = 0.25 kg

Example 3: Convert 0.035 A to milliamps (mA).

1 A = 1000 mA
0.035 A = 0.035 × 1000 = 35 mA

Example 4: Convert 6700 mm to metres.

1 m = 1000 mm
6700 mm = 6700 ÷ 1000 = 6.7 m

Example 5: Convert 2.4 MJ to joules.

1 MJ = 1 × 10⁶ J
2.4 MJ = 2.4 × 10⁶ = 2 400 000 J

Exam Tip: The most common unit conversion error in GCSE Physics exams is forgetting to convert grams to kilograms, centimetres to metres, or milliamps to amps before using an equation. Always check your units before calculating.

Standard Form

Standard form (also called scientific notation) is a way of writing very large or very small numbers. A number in standard form is written as:

A × 10ⁿ

where 1 ≤ A < 10 and n is an integer.

Examples of Standard Form

Ordinary Number	Standard Form
300 000 000 (speed of light in m/s)	3 × 10⁸
6 400 000 (radius of Earth in m)	6.4 × 10⁶
0.000 001 (1 micrometre in m)	1 × 10⁻⁶
0.000 000 000 1 (radius of an atom in m)	1 × 10⁻¹⁰
0.000 000 001 6 (charge on an electron in C)	1.6 × 10⁻¹⁹

How to Convert to Standard Form

Move the decimal point so that there is one non-zero digit before the decimal point.
Count how many places you moved the decimal point — this gives the power of 10.
If you moved the decimal point to the left, the power is positive.
If you moved the decimal point to the right, the power is negative.

Worked Example

Convert 0.000 045 m to standard form.

Move the decimal point 5 places to the right: 4.5
The power is negative (we moved right): −5
Answer: 4.5 × 10⁻⁵ m

Using Standard Form in Calculations

When multiplying or dividing numbers in standard form:

Multiplying: Multiply the numbers and add the powers.
- (3 × 10⁴) × (2 × 10³) = 6 × 10⁷
Dividing: Divide the numbers and subtract the powers.
- (8 × 10⁶) ÷ (4 × 10²) = 2 × 10⁴

Worked Example

A wire has a cross-sectional area of 2.5 × 10⁻⁶ m² and a length of 3.0 × 10² m. Calculate the volume of the wire.

Volume = area × length Volume = (2.5 × 10⁻⁶) × (3.0 × 10²) Volume = (2.5 × 3.0) × 10⁻⁶⁺² = 7.5 × 10⁻⁴ m³

Exam Tip: Make sure you can use your calculator to enter numbers in standard form. On most scientific calculators, use the EXP or ×10ˣ button. Practise this so you do not make errors in the exam.

Summary

The SI system has seven base units — the most important for GCSE Physics are the metre (m), kilogram (kg), second (s), ampere (A), and kelvin (K).
Derived units (N, J, W, Pa, Hz, C, V, Ω) are combinations of base units.
Prefixes (nano, micro, milli, centi, kilo, mega, giga) multiply or divide a unit by powers of 10.
Always convert to SI base units before substituting values into equations.
Standard form writes numbers as A × 10ⁿ where 1 ≤ A < 10 — essential for very large or very small quantities in physics.
Practise unit conversions and standard form calculations until they are automatic — these skills are tested across every topic in the course.