Units

What you'll learn

What a unit is, and why physics answers need one.
How to use the Edexcel 4PH1 units: kg, J, m, m/s, m/s², N, s and W.
How “derived units” like m/s, N, J and W are built from simpler units.
How to keep units correct in calculations.

Why units matter

A number on its own is usually not a complete physics answer. If you write “12”, it could mean 12 m, 12 s, 12 J, 12 W, or many other things. The unit tells the examiner what physical quantity you have measured or calculated.

Definition

Unit

A unit is an agreed standard used to measure a physical quantity. A physical quantity is something measurable, such as mass, time, distance, force, energy or power.

For Edexcel IGCSE Physics, you should be confident using the correct unit symbol and writing it after your numerical answer, for example 5 kg, 20 J or 8 m/s.

Key Idea

Number plus unit

In physics, a full measurement is normally a value and a unit. The value tells you “how much”; the unit tells you “of what”.

Quantity symbols and unit symbols

Physics uses letters in two different ways:

A quantity symbol is the letter used in an equation, such as $m$ for mass or $P$ for power.
A unit symbol is the abbreviation written after the number, such as kg for kilogram or W for watt.

For example, in $2.0\,\text{kg}$ , the italic $m$ is the quantity symbol for mass, while kg is the unit symbol.

Common Mistake

Capital letters matter

Use kg, m and s in lower case. Use N, J and W with capitals because their unit symbols are named after Newton, Joule and Watt.

The units in specification point 4.1

You need to be able to use these units accurately:

Physical quantity	Unit name	Unit symbol	What it measures
Mass	kilogram	kg	Amount of matter / inertia of an object
Energy or work done	joule	J	Energy stored or transferred
Distance or length	metre	m	Length, height, distance moved
Speed or velocity	metre per second	m/s	Distance travelled each second
Acceleration	metre per second squared	m/s²	Change in velocity each second
Force	newton	N	Pushes, pulls and weight
Time	second	s	Time intervals
Power	watt	W	Energy transferred each second

Some of these are simpler units, such as kg, m and s. Others are derived units, meaning they are made by combining other units through equations.

Definition

Derived unit

A derived unit is made from other units. For example, m/s is made from metres divided by seconds, because speed depends on distance and time.

The diagram shows how the units connect through common IGCSE physics equations.

Unit relationships for kg, m, s, m/s, m/s², N, J and W

The base-style units: kg, m and s

Kilogram, kg

The kilogram is the SI unit of mass. Mass is a measure of how much matter an object contains, and also how difficult it is to change its motion.

In calculations, mass should usually be in kg. If you are given grams, convert first: 1000 g = 1 kg.

Metre, m

The metre is the SI unit of distance and length. In mechanics and energy questions, distances such as height, extension and distance moved are usually measured in m.

If you are given kilometres, convert first: 1 km = 1000 m.

Second, s

The second is the SI unit of time. In calculations, time is usually measured in s, not minutes or hours.

If you are given minutes, convert first: 1 min = 60 s.

Tip

Convert before calculating

If an equation is meant to give SI units, convert to kg, m and s before substituting numbers. This makes the final unit much more likely to come out correctly.

Speed: metres per second, m/s

Speed tells you how quickly distance is covered. The unit m/s means “metres per second”: how many metres are travelled in each second.

The equation is:

average speed = distance moved ÷ time taken, $\frac{s}{t}$

where:

$v$ is average speed in m/s
$s$ is distance moved in m
$t$ is time taken in s

Example

Calculating speed in m/s

A runner travels 0.30 km in 1.5 min. Calculate the average speed in m/s.

Convert the distance and time into SI units: $0.30 \times 1000 = 300\,\text{m}$ and $1.5 \times 60 = 90\,\text{s}$ .
Use average speed = distance moved ÷ time taken, so $\frac{s}{t}$ .
Substitute the values with units: $\frac{300\,\text{m}}{90\,\text{s}} = 3.3\,\text{m/s}$ .

Tip

Read per as divided by

The word per means “for each” or “divided by”. So m/s means metres divided by seconds.

Acceleration: metres per second squared, m/s²

Acceleration is the rate of change of velocity. In other words, it tells you how quickly velocity changes.

The unit m/s² can be read as “metres per second per second”. If an object has an acceleration of 2 m/s², its velocity changes by 2 m/s every second.

The equation is:

acceleration = change in velocity ÷ time taken, $\frac{v - u}{t}$

where:

$a$ is acceleration in m/s²
$v$ is final velocity in m/s
$u$ is initial velocity in m/s
$t$ is time taken in s

Example

Calculating acceleration

A car increases its velocity from 6.0 m/s to 18 m/s in 4.0 s. Calculate its acceleration.

Find the change in velocity: $18\,\text{m/s} - 6.0\,\text{m/s} = 12\,\text{m/s}$ .
Use acceleration = change in velocity ÷ time taken, so $\frac{v - u}{t}$ .
Substitute and calculate: $\frac{12\,\text{m/s}}{4.0\,\text{s}} = 3.0\,\text{m/s}^2$ .

Common Mistake

m/s² is not m/s multiplied by 2

The ² means the seconds are squared in the denominator. m/s² means “metres per second per second”, not “metres per second times 2”.

Force: newtons, N

A force is a push or pull. Forces can change an object’s speed, direction of motion or shape. The SI unit of force is the newton, N.

The equation is:

force = mass × acceleration, $\times a$

where:

$F$ is force in N
$m$ is mass in kg
$a$ is acceleration in m/s²

This means 1 N is the force needed to give a mass of 1 kg an acceleration of 1 m/s².

Energy and work done: joules, J

Energy is measured in joules, J. Energy can be stored or transferred.

Work done is a way of transferring energy when a force moves an object through a distance. One useful unit link is:

1 J = 1 N m

So if a force of 1 N moves an object 1 m in the direction of the force, 1 J of energy is transferred.

Power: watts, W

Power is the rate of energy transfer. A more powerful device transfers energy more quickly.

The equation is:

power = energy transferred ÷ time taken, $\frac{E}{t}$

where:

$P$ is power in W
$E$ is energy transferred in J
$t$ is time taken in s

A watt means one joule per second:

1 W = 1 J/s

Common Mistake

J and W are different quantities

A joule, J, measures an amount of energy. A watt, W, measures how quickly energy is transferred. A 100 W lamp transfers 100 J of energy every second, not 100 J in total.

Example

Linking newtons, joules and watts

A 2.0 kg trolley accelerates at 1.5 m/s². The force moves it 8.0 m, and the energy transfer takes 4.0 s. Find the force, energy transferred and average power.

Use force = mass × acceleration: $\times a = 2.0\,\text{kg} \times 1.5\,\text{m/s}^2 = 3.0\,\text{N}$ .
Energy transferred by work done is force multiplied by distance moved in the direction of the force: $\times d = 3.0\,\text{N} \times 8.0\,\text{m} = 24\,\text{J}$ .
Use power = energy transferred ÷ time taken: $\frac{E}{t} = \frac{24\,\text{J}}{4.0\,\text{s}} = 6.0\,\text{W}$ .

Unit checks: a quick way to spot errors

Units often tell you whether your method makes sense.

If you divide distance in m by time in s, your answer must be in m/s. If you divide energy in J by time in s, your answer must be in W. If you multiply mass in kg by acceleration in m/s², your answer must be in N.

Key Idea

Equations create units

The unit of your answer comes from the operation in the equation. Dividing by time often gives a “per second” unit, while multiplying force by distance gives energy in joules.

Exam technique

In the exam

Write a unit with every numerical answer unless the question clearly asks for a ratio or percentage.
Convert to kg, m and s before substituting into equations, especially if the question gives g, km, minutes or hours.
Use the unit as a check: distance divided by time gives m/s, energy divided by time gives W, and mass multiplied by acceleration gives N.

Self review

Check yourself

Which unit would you use for mass, force, energy and power?
A velocity changes by 12 m/s in 3 s. What unit should the acceleration have?
Why is 200 W not the same type of quantity as 200 J?

What you'll learn

What a unit is, and why physics answers need one.
How to use the Edexcel 4PH1 units: kg, J, m, m/s, m/s², N, s and W.
How “derived units” like m/s, N, J and W are built from simpler units.
How to keep units correct in calculations.

Why units matter

Definition

Unit

A unit is an agreed standard used to measure a physical quantity. A physical quantity is something measurable, such as mass, time, distance, force, energy or power.

For Edexcel IGCSE Physics, you should be confident using the correct unit symbol and writing it after your numerical answer, for example 5 kg, 20 J or 8 m/s.

Key Idea

Number plus unit

In physics, a full measurement is normally a value and a unit. The value tells you “how much”; the unit tells you “of what”.

Quantity symbols and unit symbols

Physics uses letters in two different ways:

A quantity symbol is the letter used in an equation, such as $m$ for mass or $P$ for power.
A unit symbol is the abbreviation written after the number, such as kg for kilogram or W for watt.

For example, in $2.0\,\text{kg}$ , the italic $m$ is the quantity symbol for mass, while kg is the unit symbol.

Common Mistake

Capital letters matter

Use kg, m and s in lower case. Use N, J and W with capitals because their unit symbols are named after Newton, Joule and Watt.

The units in specification point 4.1

You need to be able to use these units accurately:

Physical quantity	Unit name	Unit symbol	What it measures
Mass	kilogram	kg	Amount of matter / inertia of an object
Energy or work done	joule	J	Energy stored or transferred
Distance or length	metre	m	Length, height, distance moved
Speed or velocity	metre per second	m/s	Distance travelled each second
Acceleration	metre per second squared	m/s²	Change in velocity each second
Force	newton	N	Pushes, pulls and weight
Time	second	s	Time intervals
Power	watt	W	Energy transferred each second

Some of these are simpler units, such as kg, m and s. Others are derived units, meaning they are made by combining other units through equations.

Definition

Derived unit

A derived unit is made from other units. For example, m/s is made from metres divided by seconds, because speed depends on distance and time.

The diagram shows how the units connect through common IGCSE physics equations.

Unit relationships for kg, m, s, m/s, m/s², N, J and W

The base-style units: kg, m and s

Kilogram, kg

The kilogram is the SI unit of mass. Mass is a measure of how much matter an object contains, and also how difficult it is to change its motion.

In calculations, mass should usually be in kg. If you are given grams, convert first: 1000 g = 1 kg.

Metre, m

The metre is the SI unit of distance and length. In mechanics and energy questions, distances such as height, extension and distance moved are usually measured in m.

If you are given kilometres, convert first: 1 km = 1000 m.

Second, s

The second is the SI unit of time. In calculations, time is usually measured in s, not minutes or hours.

If you are given minutes, convert first: 1 min = 60 s.

Tip

Convert before calculating

If an equation is meant to give SI units, convert to kg, m and s before substituting numbers. This makes the final unit much more likely to come out correctly.

Speed: metres per second, m/s

Speed tells you how quickly distance is covered. The unit m/s means “metres per second”: how many metres are travelled in each second.

The equation is:

average speed = distance moved ÷ time taken, $\frac{s}{t}$

where:

$v$ is average speed in m/s
$s$ is distance moved in m
$t$ is time taken in s

Example

Calculating speed in m/s

A runner travels 0.30 km in 1.5 min. Calculate the average speed in m/s.

Convert the distance and time into SI units: $0.30 \times 1000 = 300\,\text{m}$ and $1.5 \times 60 = 90\,\text{s}$ .
Use average speed = distance moved ÷ time taken, so $\frac{s}{t}$ .
Substitute the values with units: $\frac{300\,\text{m}}{90\,\text{s}} = 3.3\,\text{m/s}$ .

Tip

Read per as divided by

The word per means “for each” or “divided by”. So m/s means metres divided by seconds.

Acceleration: metres per second squared, m/s²

Acceleration is the rate of change of velocity. In other words, it tells you how quickly velocity changes.

The unit m/s² can be read as “metres per second per second”. If an object has an acceleration of 2 m/s², its velocity changes by 2 m/s every second.

The equation is:

acceleration = change in velocity ÷ time taken, $\frac{v - u}{t}$

where:

$a$ is acceleration in m/s²
$v$ is final velocity in m/s
$u$ is initial velocity in m/s
$t$ is time taken in s

Example

Calculating acceleration

A car increases its velocity from 6.0 m/s to 18 m/s in 4.0 s. Calculate its acceleration.

Find the change in velocity: $18\,\text{m/s} - 6.0\,\text{m/s} = 12\,\text{m/s}$ .
Use acceleration = change in velocity ÷ time taken, so $\frac{v - u}{t}$ .
Substitute and calculate: $\frac{12\,\text{m/s}}{4.0\,\text{s}} = 3.0\,\text{m/s}^2$ .

Common Mistake

m/s² is not m/s multiplied by 2

The ² means the seconds are squared in the denominator. m/s² means “metres per second per second”, not “metres per second times 2”.

Force: newtons, N

A force is a push or pull. Forces can change an object’s speed, direction of motion or shape. The SI unit of force is the newton, N.

The equation is:

force = mass × acceleration, $\times a$

where:

$F$ is force in N
$m$ is mass in kg
$a$ is acceleration in m/s²

This means 1 N is the force needed to give a mass of 1 kg an acceleration of 1 m/s².

Energy and work done: joules, J

Energy is measured in joules, J. Energy can be stored or transferred.

Work done is a way of transferring energy when a force moves an object through a distance. One useful unit link is:

1 J = 1 N m

So if a force of 1 N moves an object 1 m in the direction of the force, 1 J of energy is transferred.

Power: watts, W

Power is the rate of energy transfer. A more powerful device transfers energy more quickly.

The equation is:

power = energy transferred ÷ time taken, $\frac{E}{t}$

where:

$P$ is power in W
$E$ is energy transferred in J
$t$ is time taken in s

A watt means one joule per second:

1 W = 1 J/s

Common Mistake

J and W are different quantities

A joule, J, measures an amount of energy. A watt, W, measures how quickly energy is transferred. A 100 W lamp transfers 100 J of energy every second, not 100 J in total.

Example

Linking newtons, joules and watts

A 2.0 kg trolley accelerates at 1.5 m/s². The force moves it 8.0 m, and the energy transfer takes 4.0 s. Find the force, energy transferred and average power.

Use force = mass × acceleration: $\times a = 2.0\,\text{kg} \times 1.5\,\text{m/s}^2 = 3.0\,\text{N}$ .
Energy transferred by work done is force multiplied by distance moved in the direction of the force: $\times d = 3.0\,\text{N} \times 8.0\,\text{m} = 24\,\text{J}$ .
Use power = energy transferred ÷ time taken: $\frac{E}{t} = \frac{24\,\text{J}}{4.0\,\text{s}} = 6.0\,\text{W}$ .

Unit checks: a quick way to spot errors

Units often tell you whether your method makes sense.

Key Idea

Equations create units

The unit of your answer comes from the operation in the equation. Dividing by time often gives a “per second” unit, while multiplying force by distance gives energy in joules.

Exam technique

In the exam

Write a unit with every numerical answer unless the question clearly asks for a ratio or percentage.
Convert to kg, m and s before substituting into equations, especially if the question gives g, km, minutes or hours.
Use the unit as a check: distance divided by time gives m/s, energy divided by time gives W, and mass multiplied by acceleration gives N.

Self review

Check yourself

Which unit would you use for mass, force, energy and power?
A velocity changes by 12 m/s in 3 s. What unit should the acceleration have?
Why is 200 W not the same type of quantity as 200 J?

What you'll learn

Why units matter

Quantity symbols and unit symbols

The units in specification point 4.1

The base-style units: kg, m and s

Kilogram, kg

Metre, m

Second, s

Speed: metres per second, m/s

Acceleration: metres per second squared, m/s²

Force: newtons, N

Energy and work done: joules, J

Power: watts, W

Unit checks: a quick way to spot errors

Review Units by teaching Genie

Remember key concepts with flashcards

Units

What you'll learn

Why units matter

Quantity symbols and unit symbols

The units in specification point 4.1

The base-style units: kg, m and s

Kilogram, kg

Metre, m

Second, s

Speed: metres per second, m/s

Acceleration: metres per second squared, m/s²

Force: newtons, N

Energy and work done: joules, J

Power: watts, W

Unit checks: a quick way to spot errors

Review Units by teaching Genie

Remember key concepts with flashcards

Units

What you'll learn

Why units matter

Quantity symbols and unit symbols

The units in specification point 4.1

The base-style units: kg, m and s

Kilogram, kg

Metre, m

Second, s

Speed: metres per second, m/s

Acceleration: metres per second squared, m/s²

Force: newtons, N

Energy and work done: joules, J

Power: watts, W

Unit checks: a quick way to spot errors

Review Units by teaching Genie

Remember key concepts with flashcards

Units Revision Guide

Units

What you'll learn

Why units matter

Quantity symbols and unit symbols

The units in specification point 4.1

The base-style units: kg, m and s

Kilogram, kg

Metre, m

Second, s

Speed: metres per second, m/s

Acceleration: metres per second squared, m/s²

Force: newtons, N

Energy and work done: joules, J

Power: watts, W

Unit checks: a quick way to spot errors

Review Units by teaching Genie

Remember key concepts with flashcards

Units Revision Guide