Physics prefixes

Physics prefixes are the letters in front of a unit that multiply it by a power of ten: the k in km means × 10³, and the n in nm means × 10⁻⁹. For GCSE Physics, AQA lists tera, giga, mega, kilo, centi, milli, micro and nano. A-level adds pico and femto. To convert, replace the prefix with its power of ten, so 520 nm = 520 × 10⁻⁹ m = 5.2 × 10⁻⁷ m.

List of physics prefixes

Apart from centi, the prefixes you need go up or down in steps of 1,000, that is 10³. The symbol for micro is the Greek letter mu, μ. Capital and lower case letters matter: M is mega but m is milli, so 1 MW is a thousand million times bigger than 1 mW.

How to convert units with prefixes

There are two directions, and both are about swapping the prefix for its power of ten:

• From a prefix to the base unit: multiply by the power of ten. 3.6 kJ = 3.6 × 10³ J = 3,600 J. 15 mA = 15 × 10⁻³ A = 0.015 A.
• From the base unit to a prefix: divide by the power of ten. 0.000 08 m = 0.000 08 ÷ 10⁻⁶ μm = 80 μm. 2,500,000 W = 2,500,000 ÷ 10⁶ MW = 2.5 MW.

A quick check: a bigger prefix always means a smaller number in front. 2.5 MW and 2,500,000 W are the same power. Before you put numbers into a physics equation, convert every quantity to base SI units (m, kg, s, A, J, W, V, Ω) unless you know the units cancel.

Practise moving between powers of ten in this question from the Smallest Thing course.

Prefixes in each physics topic

Squared and cubed units

Areas and volumes catch a lot of people out, because the prefix is squared or cubed along with the unit:

• 1 cm = 10⁻² m, so 1 cm² = (10⁻² m)² = 10⁻⁴ m².
• 1 cm³ = (10⁻² m)³ = 10⁻⁶ m³, so 1,000,000 cm³ make 1 m³.
• 1 mm² = (10⁻³ m)² = 10⁻⁶ m², which matters for the cross-sectional area of a wire.

So a density of 1 g/cm³ is 10⁻³ kg ÷ 10⁻⁶ m³ = 1,000 kg/m³.

Worked examples

Example 1: wavelength of light

Green light has a wavelength of 520 nm. Write this in metres in standard form.

• nano means × 10⁻⁹, so 520 nm = 520 × 10⁻⁹ m.
• In standard form: 5.2 × 10⁻⁷ m.

Example 2: energy from a kettle

A kettle with a power of 2.4 kW is switched on for 3.0 minutes. How much energy does it transfer, in kJ?

1. Convert to base units: P = 2.4 kW = 2,400 W and t = 3.0 × 60 = 180 s.
2. E = P × t = 2,400 × 180 = 432,000 J.
3. Divide by 10³ for kJ: 432 kJ (or 0.432 MJ).

Example 3: milliamps and kilohms

A current of 2.0 mA flows through a 4.7 kΩ resistor. Find the potential difference across it.

1. I = 2.0 mA = 2.0 × 10⁻³ A and R = 4.7 kΩ = 4.7 × 10³ Ω.
2. V = I × R = 2.0 × 10⁻³ × 4.7 × 10³ = 9.4 V.
3. The 10⁻³ and 10³ cancel, which is why mA × kΩ gives volts directly.

Example 4: pressure on a small area

A force of 60 N acts on an area of 25 cm². Find the pressure in kPa.

1. Area = 25 cm² = 25 × 10⁻⁴ m² = 0.0025 m².
2. p = F ÷ A = 60 ÷ 0.0025 = 24,000 Pa.
3. Divide by 10³: 24 kPa.

Check standard form answers with the Scientific Notation Calculator, and see standard form for the maths behind it.

Typing prefixes into a calculator

Use the ×10^x button (EXP or EE on some calculators) for the power of ten. For 4.7 kΩ, type 4.7 ×10^x 3. For 520 nm, type 520 ×10^x (−) 9, using the negative key rather than the subtract key. This keeps the whole number together, so the calculator does not split the sum in the wrong place.

Common mistakes

• Mixing up M and m. M is mega, 10⁶; m is milli, 10⁻³ (and also the symbol for metre).
• Writing K for kilo. The symbol is a lower case k. Capital K is kelvin.
• Converting cm² as if it were cm. 1 cm² is 10⁻⁴ m², not 10⁻² m².
• Forgetting to convert before using an equation. Minutes to seconds and kW to W come first.
• Going the wrong way. If the number got smaller when you moved to a smaller prefix, you divided instead of multiplying.
• Confusing μ with m or u. Write the μ clearly; a misread prefix is a factor of 1,000 out.

Practise with a short timed paper

Prefixes and unit conversions come up across every topic in GCSE Physics. The daily GCSE Physics Higher paper is a short timed paper of 8 questions, with a new one every day.

Read next

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