Physics SI Units, Prefixes, and Conversions: A Quick-Check Guide for Exams

Overview

In physics revision, students often focus on memorising equations and definitions, but units are just as important. They tell you what a quantity means, whether an answer is sensible, and whether a substitution into an equation is valid. Many exam questions are designed so that the physics is straightforward once the units are handled properly. That is why unit conversions physics questions appear across forces, electricity, waves, energy, practical work, and data analysis.

This guide is built as a reusable reference page. You can come back to it when you need to check a prefix, convert between common forms, or remind yourself which standard units in physics belong with which quantities. The aim is not to list every possible unit in the SI system. Instead, it focuses on the units and conversions that appear repeatedly in school and introductory university physics.

The main rule is simple: before using an equation, check whether the values are already in SI units physics expects. If they are not, convert first. In many cases that means:

• centimetres to metres
• grams to kilograms
• minutes to seconds
• milliseconds to seconds
• kilovolts to volts
• milliamps to amps

That one habit removes a large number of avoidable marks lost in exams.

If you are also revising graph work, it helps to pair this topic with How to Draw and Interpret Physics Graphs: Gradient, Area Under the Curve, and Best Fit, because graph axes and gradients often depend on unit conversion.

Core framework

The quickest way to become reliable with physics prefixes and conversions is to learn a compact framework rather than treating every question as new. Use the four-step check below.

1. Identify the physical quantity

Read the symbol and the wording carefully. For example, v may be velocity, V may be potential difference, and m may mean mass or metre depending on context. A surprising number of errors come from recognising the equation but not the quantity.

2. Recall the standard SI unit

Most school-level calculations expect base or derived SI units. Here are the core ones worth knowing well:

• Length: metre, m
• Mass: kilogram, kg
• Time: second, s
• Current: ampere, A
• Temperature: kelvin, K
• Amount of substance: mole, mol
• Luminous intensity: candela, cd

From these base units come common derived units used in physics revision:

• Speed or velocity: metres per second, m/s
• Acceleration: metres per second squared, m/s²
• Force: newton, N
• Energy or work: joule, J
• Power: watt, W
• Pressure: pascal, Pa
• Charge: coulomb, C
• Potential difference: volt, V
• Resistance: ohm, Ω
• Frequency: hertz, Hz

You do not always need to break derived units down into base units to solve a problem, but it can help you check whether an equation is consistent. For example:

• 1 N = 1 kg m/s²
• 1 J = 1 N m
• 1 W = 1 J/s
• 1 Pa = 1 N/m²

3. Check for prefixes

Prefixes scale a unit by a power of ten. In exam questions, the most useful prefixes are:

• kilo, k = 10³ = 1000
• centi, c = 10⁻² = 0.01
• milli, m = 10⁻³ = 0.001
• micro, μ = 10⁻⁶ = 0.000001
• nano, n = 10⁻⁹ = 0.000000001
• mega, M = 10⁶ = 1000000
• giga, G = 10⁹ = 1000000000

These are especially common in electricity, waves, and modern physics:

• mA to A
• kV to V
• ms to s
• μs to s
• nm to m
• MHz to Hz
• kΩ to Ω

Be careful: uppercase and lowercase matter. M means mega, while m means milli when used as a prefix and metre when used as a unit symbol. Context matters.

4. Convert using powers of ten, then substitute

A reliable method is:

1. Write the original value.
2. Write the conversion factor.
3. Convert into the standard unit.
4. Only then put the number into the equation.

For example:

35 cm = 35 ÷ 100 m = 0.35 m

4.2 ms = 4.2 × 10⁻³ s = 0.0042 s

3.5 kV = 3.5 × 10³ V = 3500 V

250 mA = 250 × 10⁻³ A = 0.250 A

This method slows you down slightly at first, but it is much safer than trying to convert mentally while solving.

A quick reference table

Below are the conversions that appear often enough to justify automatic recall:

• 1 km = 1000 m
• 1 cm = 0.01 m
• 1 mm = 0.001 m
• 1 g = 0.001 kg
• 1 min = 60 s
• 1 h = 3600 s
• 1 mA = 0.001 A
• 1 kV = 1000 V
• 1 kW = 1000 W
• 1 MHz = 1,000,000 Hz
• 1 nm = 1 × 10⁻⁹ m
• 1 cm² = 1 × 10⁻⁴ m²
• 1 cm³ = 1 × 10⁻⁶ m³

The last two are especially important because area and volume conversions are often mishandled. When the unit is squared or cubed, the conversion factor is squared or cubed as well.

Practical examples

The best way to make physics units revision useful is to see how it changes actual exam working. These examples show the thinking you should aim to reproduce.

Example 1: Speed from distance and time

A car travels 150 m in 12 s. Find its speed.

Equation: speed = distance ÷ time

The units are already SI:

• distance in m
• time in s

So:

speed = 150 ÷ 12 = 12.5 m/s

This is straightforward, but it is worth noticing why: there was no need to convert first.

Example 2: Speed with a hidden conversion

A runner covers 100 m in 12.4 s. What is the average speed in km/h?

First find speed in the standard unit:

speed = 100 ÷ 12.4 = 8.06 m/s

Now convert m/s to km/h. Since 1 m/s = 3.6 km/h:

speed = 8.06 × 3.6 = 29.0 km/h approximately

In many school physics questions, the expected standard answer is m/s unless the question explicitly requests a different unit. Read the final instruction carefully.

Example 3: Current conversion in electricity

A component has a current of 250 mA and a potential difference of 12 V. Find the power.

Equation: power = current × potential difference

Convert current first:

250 mA = 0.250 A

Then substitute:

P = 0.250 × 12 = 3.0 W

If you skip the conversion and use 250 as if it were amps, your answer becomes 3000 W, which is three orders of magnitude too large.

For more circuit practice, see GCSE Electricity Revision: Equations, Circuits, Power, and Resistance or A-Level Electricity Revision: EMF, Internal Resistance, Potential Dividers, and Circuit Analysis.

Example 4: Wave speed

A wave has frequency 2.5 kHz and wavelength 0.12 m. Find the wave speed.

Equation: wave speed = frequency × wavelength

Convert frequency:

2.5 kHz = 2500 Hz

Now substitute:

v = 2500 × 0.12 = 300 m/s

This is a common pattern in waves questions: the wavelength is often already in metres, while frequency may appear in kHz or MHz.

Related revision pages include GCSE Waves Revision: Wave Speed, Properties, Required Practical Links, and Exam Questions and A-Level Waves Revision: Superposition, Stationary Waves, Diffraction, and Refraction.

Example 5: Density and unit choice

A block has mass 320 g and volume 40 cm³. Find its density in kg/m³.

Equation: density = mass ÷ volume

Convert each quantity:

• 320 g = 0.320 kg
• 40 cm³ = 40 × 10⁻⁶ m³ = 4.0 × 10⁻⁵ m³

Then:

density = 0.320 ÷ 4.0 × 10⁻⁵ = 8000 kg/m³

This example shows why volume conversions need care. Since 1 cm = 10⁻² m, then 1 cm³ = (10⁻²)³ m³ = 10⁻⁶ m³.

Example 6: Force from acceleration

A trolley of mass 750 g accelerates at 2.4 m/s². Find the resultant force.

Equation: force = mass × acceleration

Convert mass:

750 g = 0.750 kg

Then:

F = 0.750 × 2.4 = 1.8 N

Mass must be in kilograms for the newton to work correctly in this standard form.

This links closely with GCSE Forces and Motion Revision: Distance-Time Graphs, Speed, Velocity, and Acceleration.

Example 7: Using units to check an answer

Suppose you calculate resistance from potential difference and current:

R = V ÷ I

If voltage is in volts and current is in amps, the answer should come out in ohms. If your calculator gives a number and you label it in joules or watts, that is a sign to stop and review. Unit sense-checking is a powerful exam technique because it catches mistakes before you move on.

Example 8: Practical work and graphs

In a required practical, you might record length in cm but need to plot in m to match theory. If your graph gradient is supposed to represent a physical constant, inconsistent axis units can make the final value look wrong even when your graph line is tidy. That is one reason practical analysis and units belong together. If you need support with method and uncertainties, see A-Level Physics Required Practicals Explained: Core Methods, Uncertainties, and Analysis.

Common mistakes

Most unit errors are predictable. If you know the common traps, you can check for them quickly under exam pressure.

Forgetting to convert before substitution

This is the most common mistake. Students often write the correct equation and then immediately substitute values with mixed units. Build the habit of pausing for five seconds to check every quantity.

Confusing milli and mega

Lowercase m means milli, 10⁻³. Uppercase M means mega, 10⁶. These differ by a factor of a billion. In electricity and waves, this matters a lot.

Mixing g and kg

In mechanics, mass should usually be in kilograms. Using grams in equations such as F = ma or E = mcΔθ gives answers that are too large or too small by a factor of 1000.

Missing square and cube conversions

Area and volume are frequent trouble spots:

• 1 cm² is not 0.01 m²; it is 0.0001 m²
• 1 cm³ is not 0.01 m³; it is 0.000001 m³

If the unit is squared or cubed, the conversion factor must be squared or cubed too.

Not reading the final unit requested

Sometimes the working should be done in SI units, but the final answer needs to be presented in a different unit. For example, a question may ask for speed in km/h or energy in kJ. The safest approach is:

1. convert into SI units
2. calculate
3. convert the final answer if needed

Treating unit symbols like abbreviations

Unit symbols follow standard forms. Write 5 m, 3.2 A, 12 V, 50 Hz. Do not add full stops, and do not invent mixed formats. Clear notation makes your working easier to follow.

Ignoring significant figures and sensible scale

Units and magnitude belong together. If a household resistor appears to have a resistance of 0.000004 Ω, or a walking speed comes out as 400 m/s, the number should prompt a recheck. Your physical sense is a tool, not an extra.

For broader exam-writing habits, How to Answer 6 Mark Physics Questions: A GCSE and A-Level Exam Technique Guide can help you present method and reasoning more clearly.

When to revisit

This topic is worth revisiting regularly because it supports nearly every calculation-heavy part of physics revision. You do not need a long relearning session each time. A short targeted check is usually enough.

Come back to this guide when:

• you start a new topic with unfamiliar quantities, such as waves, electricity, or radioactivity
• you notice repeated arithmetic errors in past paper work
• you are practising required practical physics and need consistent graph axes or processed data
• you move from GCSE physics revision into A-Level physics revision and meet a wider range of prefixes
• you are reviewing mark schemes and see that method marks were available but the final answer was wrong through units

A practical routine is to keep a one-page units sheet beside you during problem practice. Include:

• the common prefixes from nano to giga
• the standard SI unit for each major quantity
• the conversions you personally forget most often
• one reminder about squared and cubed units

You can also build a short self-check before submitting any answer:

1. Have I used standard units in physics for the equation?
2. Did I convert prefixes correctly?
3. Does the final unit match the quantity asked for?
4. Is the size of the answer reasonable?

If you are planning revision across the full course, use this guide alongside GCSE Physics Topics List with Revision Priority, Key Equations, and Common Mistakes or A-Level Physics Topics List with Best Revision Order and High-Value Skills. Units are not a separate topic to finish once and forget. They are a core exam skill that should stay active throughout your revision.

Finally, if your school, exam board, calculator habits, or practical methods change, revisit your unit sheet and update it. The most useful reference page is the one you actually return to under pressure. Keep it short, accurate, and visible while you practise physics worked solutions.