Units

What you'll learn

What a unit is and why physics answers need one.
The key units in spec point 8.1: kg, m, m/s, m/s², N, s and N/kg.
How to connect each unit to the physical quantity it measures.
How to avoid common unit mistakes in calculations.

Why units matter

In physics, a number on its own is usually incomplete. If you write “the distance is 5”, that could mean 5 m, 5 km, or even 5 s if you have mixed up the quantity.

A quantity is something you can measure, such as mass, distance, time, speed or force. A unit tells you the scale used to measure that quantity.

Definition

Unit

A unit is a standard amount used to measure a physical quantity. For example, metre (m) is the unit for distance, and second (s) is the unit for time.

Key Idea

Numbers need units

In IGCSE Physics, an answer like “12” is usually not enough. You need the correct unit, such as 12 m, 12 s, 12 N or 12 m/s.

SI units

The units used in the specification are mostly SI units. SI stands for Système International, meaning the international system of units.

This matters because scientists around the world need to compare measurements reliably. If one person uses metres and another uses miles, calculations become much easier to get wrong.

Some SI units are base units, such as:

kilogram (kg) for mass
metre (m) for length or distance
second (s) for time

Other units are derived units, made by combining base units. For example, metre/second (m/s) combines metres and seconds.

The main units in 8.1

You need to be comfortable using these units:

Physical quantity	Unit name	Unit symbol	Meaning
mass	kilogram	kg	how much matter an object contains
distance or displacement	metre	m	length or how far something is from a point
time	second	s	duration of an event
speed or velocity	metre/second	m/s	distance travelled each second
acceleration	metre/second squared	m/s²	change in velocity each second
force	newton	N	push or pull on an object
gravitational field strength	newton/kilogram	N/kg	force of gravity per kilogram of mass

Common Mistake

Unit symbols are case-sensitive

Do not write kg as Kg, or newton as n. The correct symbols are kg and N. Capital letters matter in physics units.

Kilogram, kg: unit of mass

Mass is the amount of matter in an object. It is measured in kilograms, kg.

Mass is not the same as weight. Your mass would be the same on Earth and on the Moon, but your weight would be different because the gravitational field strength is different.

Definition

Mass

Mass is a measure of how much matter an object contains. The SI unit of mass is the kilogram, kg.

A typical school bag might have a mass of about 5 kg. A person might have a mass of about 60 kg. A planet or star has a much larger mass, so standard form is often useful in astrophysics.

Metre, m: unit of distance

Distance is how far something has moved or how far apart two points are. It is measured in metres, m.

In astrophysics, distances can be huge, so you may also meet kilometres, km. But the spec point here expects you to use metres, m, when working in standard SI units.

Definition

Distance

Distance is how far an object moves or how far apart two points are. The SI unit of distance is the metre, m.

Tip

Kilometres to metres

1 km = 1000 m. So to convert km to m, multiply by 1000.

Example

Converting kilometres to metres

A satellite travels 42 km along part of its orbit. Convert this distance into metres.

Use the conversion: 1 km = 1000 m.
Multiply the distance in km by 1000:
$m42\ \text{km} = 42 \times 1000\ \text{m}$
Calculate the value:
$42 \times 1000\ \text{m} = 42\,000\ \text{m}$

So 42 km = 42 000 m.

Second, s: unit of time

Time is how long an event lasts. It is measured in seconds, s.

In questions, time may be given in minutes or hours. You often need to convert it into seconds before using equations involving speed or acceleration.

Definition

Time

Time is the duration of an event. The SI unit of time is the second, s.

Useful conversions:

1 minute = 60 s
1 hour = 60 minutes = 3600 s

Example

Converting minutes to seconds

A measurement lasts for 8 minutes. Convert this time into seconds.

Use the conversion: 1 minute = 60 s.
Multiply by 60:
$s8\ \text{minutes} = 8 \times 60\ \text{s}$
Calculate:
$\times 60\ \text{s} = 480\ \text{s}$

So 8 minutes = 480 s.

Metre/second, m/s: unit of speed and velocity

Speed tells you how quickly distance is covered. Its unit is metre/second, written m/s. This means “metres per 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

Definition

Metre/second

A speed of 1 m/s means an object travels 1 metre every second.

Example

Calculating speed with units

A rover travels 150 m in 25 s. Calculate its average speed.

Choose the equation linking speed, distance and time:
$\frac{s}{t}$
Substitute the values with units:
$\frac{150\ \text{m}}{25\ \text{s}}$
Calculate the speed and keep the unit:
$6\ \text{m/s}$

The rover’s average speed is 6 m/s.

Common Mistake

Do not write mps

The accepted unit symbol is m/s, not mps. The slash means “per”, so m/s means metres per second.

Metre/second squared, m/s²: unit of acceleration

Acceleration is the rate of change of velocity. It tells you how much velocity changes each 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

Definition

Metre/second squared

An acceleration of 1 m/s² means the velocity changes by 1 m/s every second.

The unit m/s² can look strange at first. Read it as “metres per second per second”. It is not a speed; it is how quickly the speed or velocity is changing.

Example

Calculating acceleration with units

A small spacecraft increases its velocity from 12 m/s to 32 m/s in 5 s. Calculate its acceleration.

Find the change in velocity:
$32\ \text{m/s} - 12\ \text{m/s} = 20\ \text{m/s}$
Use the acceleration equation:
$\frac{v - u}{t}$
Substitute and calculate:
$\frac{20\ \text{m/s}}{5\ \text{s}} = 4\ \text{m/s}^2$

The spacecraft’s acceleration is 4 m/s².

Tip

Speed unit versus acceleration unit

m/s is for speed or velocity.
m/s² is for acceleration.
If a question asks how quickly velocity changes, the answer should be in m/s², not m/s.

Newton, N: unit of force

A force is a push or pull on an object. Force is measured in newtons, 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

Definition

Newton

One newton is the force needed to give a mass of 1 kg an acceleration of 1 m/s².

This means the newton is a derived unit. It is connected to kg, m and s through the equation for force.

Example

Calculating force with units

An object of mass 8 kg accelerates at 3 m/s². Calculate the resultant force on it.

Use the force equation:
$\times a$
Substitute the mass and acceleration:
$8\ \text{kg} \times 3\ \text{m/s}^2$
Calculate the force:
$24\ \text{N}$

The resultant force is 24 N.

Common Mistake

Confusing mass and force

Mass is measured in kg. Force is measured in N. Weight is a force, so weight must be measured in N, not kg.

Newton/kilogram, N/kg: unit of gravitational field strength

Gravitational field strength tells you how much gravitational force acts on each kilogram of mass. It is measured in newtons per kilogram, N/kg.

The equation is:

weight = mass × gravitational field strength

\times g

where:

$W$ is weight in N
$m$ is mass in kg
$g$ is gravitational field strength in N/kg

Definition

Gravitational field strength

Gravitational field strength is the force of gravity per kilogram of mass at a point. Its unit is N/kg.

On Earth, gravitational field strength is about 10 N/kg at IGCSE level. That means each kilogram of mass experiences about 10 N of weight.

Example

Calculating gravitational field strength

An astronaut has a mass of 70 kg. On a planet, their weight is 280 N. Calculate the planet’s gravitational field strength.

Rearrange the equation $\times g$ to make $g$ the subject:
$\frac{W}{m}$
Substitute the values with units:
$\frac{280\ \text{N}}{70\ \text{kg}}$
Calculate the gravitational field strength:
$4\ \text{N/kg}$

The planet’s gravitational field strength is 4 N/kg.

Key Idea

N/kg and m/s² are linked

Gravitational field strength can be measured in N/kg, and acceleration can be measured in m/s². These units are closely related, but in this specification you should use N/kg for gravitational field strength and m/s² for acceleration.

Choosing the correct unit

A good way to choose a unit is to ask: “What type of quantity is this?”

If the question asks for...	Use this unit
mass	kg
distance, height or radius	m
time	s
speed or velocity	m/s
acceleration	m/s²
force, weight or thrust	N
gravitational field strength	N/kg

Example

Selecting units from quantities

A question gives the mass of a probe, the force on it and the time taken for a signal to arrive. State suitable units for each quantity.

Mass is the amount of matter, so its unit is kg.
Force is a push or pull, so its unit is N.
Time is a duration, so its unit is s.

The suitable units are kg, N and s.

Unit discipline in calculations

In longer questions, especially in astrophysics, you may need to calculate with very large distances or times. The method is the same: use the correct equation, substitute values with units, and check the final unit.

Tip

A quick unit check

If you divide metres by seconds, the unit must be m/s. If you multiply kilograms by m/s², the unit must be N.

Common Mistake

Convert before calculating

If an equation needs SI units, convert first. For example, use metres instead of kilometres and seconds instead of minutes unless the question clearly allows another unit.

Exam technique

In the exam

Identify the quantity being asked for first, then choose the matching unit: kg, m, s, m/s, m/s², N or N/kg.
In calculations, write units in your substitution line so you are less likely to mix up mass, weight, speed or acceleration.
Check whether any values need converting, especially km to m or minutes to seconds.

Self review

Check yourself

What is the difference between the units kg and N?
Why is acceleration measured in m/s² rather than m/s?
A planet has gravitational field strength 6 N/kg. What does that mean in words?

What you'll learn

What a unit is and why physics answers need one.
The key units in spec point 8.1: kg, m, m/s, m/s², N, s and N/kg.
How to connect each unit to the physical quantity it measures.
How to avoid common unit mistakes in calculations.

Why units matter

In physics, a number on its own is usually incomplete. If you write “the distance is 5”, that could mean 5 m, 5 km, or even 5 s if you have mixed up the quantity.

A quantity is something you can measure, such as mass, distance, time, speed or force. A unit tells you the scale used to measure that quantity.

Definition

Unit

A unit is a standard amount used to measure a physical quantity. For example, metre (m) is the unit for distance, and second (s) is the unit for time.

Key Idea

Numbers need units

In IGCSE Physics, an answer like “12” is usually not enough. You need the correct unit, such as 12 m, 12 s, 12 N or 12 m/s.

SI units

The units used in the specification are mostly SI units. SI stands for Système International, meaning the international system of units.

This matters because scientists around the world need to compare measurements reliably. If one person uses metres and another uses miles, calculations become much easier to get wrong.

Some SI units are base units, such as:

kilogram (kg) for mass
metre (m) for length or distance
second (s) for time

Other units are derived units, made by combining base units. For example, metre/second (m/s) combines metres and seconds.

The main units in 8.1

You need to be comfortable using these units:

Physical quantity	Unit name	Unit symbol	Meaning
mass	kilogram	kg	how much matter an object contains
distance or displacement	metre	m	length or how far something is from a point
time	second	s	duration of an event
speed or velocity	metre/second	m/s	distance travelled each second
acceleration	metre/second squared	m/s²	change in velocity each second
force	newton	N	push or pull on an object
gravitational field strength	newton/kilogram	N/kg	force of gravity per kilogram of mass

Common Mistake

Unit symbols are case-sensitive

Do not write kg as Kg, or newton as n. The correct symbols are kg and N. Capital letters matter in physics units.

Kilogram, kg: unit of mass

Mass is the amount of matter in an object. It is measured in kilograms, kg.

Mass is not the same as weight. Your mass would be the same on Earth and on the Moon, but your weight would be different because the gravitational field strength is different.

Definition

Mass

Mass is a measure of how much matter an object contains. The SI unit of mass is the kilogram, kg.

A typical school bag might have a mass of about 5 kg. A person might have a mass of about 60 kg. A planet or star has a much larger mass, so standard form is often useful in astrophysics.

Metre, m: unit of distance

Distance is how far something has moved or how far apart two points are. It is measured in metres, m.

In astrophysics, distances can be huge, so you may also meet kilometres, km. But the spec point here expects you to use metres, m, when working in standard SI units.

Definition

Distance

Distance is how far an object moves or how far apart two points are. The SI unit of distance is the metre, m.

Tip

Kilometres to metres

1 km = 1000 m. So to convert km to m, multiply by 1000.

Example

Converting kilometres to metres

A satellite travels 42 km along part of its orbit. Convert this distance into metres.

Use the conversion: 1 km = 1000 m.
Multiply the distance in km by 1000:
$m42\ \text{km} = 42 \times 1000\ \text{m}$
Calculate the value:
$42 \times 1000\ \text{m} = 42\,000\ \text{m}$

So 42 km = 42 000 m.

Second, s: unit of time

Time is how long an event lasts. It is measured in seconds, s.

In questions, time may be given in minutes or hours. You often need to convert it into seconds before using equations involving speed or acceleration.

Definition

Time

Time is the duration of an event. The SI unit of time is the second, s.

Useful conversions:

1 minute = 60 s
1 hour = 60 minutes = 3600 s

Example

Converting minutes to seconds

A measurement lasts for 8 minutes. Convert this time into seconds.

Use the conversion: 1 minute = 60 s.
Multiply by 60:
$s8\ \text{minutes} = 8 \times 60\ \text{s}$
Calculate:
$\times 60\ \text{s} = 480\ \text{s}$

So 8 minutes = 480 s.

Metre/second, m/s: unit of speed and velocity

Speed tells you how quickly distance is covered. Its unit is metre/second, written m/s. This means “metres per 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

Definition

Metre/second

A speed of 1 m/s means an object travels 1 metre every second.

Example

Calculating speed with units

A rover travels 150 m in 25 s. Calculate its average speed.

Choose the equation linking speed, distance and time:
$\frac{s}{t}$
Substitute the values with units:
$\frac{150\ \text{m}}{25\ \text{s}}$
Calculate the speed and keep the unit:
$6\ \text{m/s}$

The rover’s average speed is 6 m/s.

Common Mistake

Do not write mps

The accepted unit symbol is m/s, not mps. The slash means “per”, so m/s means metres per second.

Metre/second squared, m/s²: unit of acceleration

Acceleration is the rate of change of velocity. It tells you how much velocity changes each 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

Definition

Metre/second squared

An acceleration of 1 m/s² means the velocity changes by 1 m/s every second.

The unit m/s² can look strange at first. Read it as “metres per second per second”. It is not a speed; it is how quickly the speed or velocity is changing.

Example

Calculating acceleration with units

A small spacecraft increases its velocity from 12 m/s to 32 m/s in 5 s. Calculate its acceleration.

Find the change in velocity:
$32\ \text{m/s} - 12\ \text{m/s} = 20\ \text{m/s}$
Use the acceleration equation:
$\frac{v - u}{t}$
Substitute and calculate:
$\frac{20\ \text{m/s}}{5\ \text{s}} = 4\ \text{m/s}^2$

The spacecraft’s acceleration is 4 m/s².

Tip

Speed unit versus acceleration unit

m/s is for speed or velocity.
m/s² is for acceleration.
If a question asks how quickly velocity changes, the answer should be in m/s², not m/s.

Newton, N: unit of force

A force is a push or pull on an object. Force is measured in newtons, 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

Definition

Newton

One newton is the force needed to give a mass of 1 kg an acceleration of 1 m/s².

This means the newton is a derived unit. It is connected to kg, m and s through the equation for force.

Example

Calculating force with units

An object of mass 8 kg accelerates at 3 m/s². Calculate the resultant force on it.

Use the force equation:
$\times a$
Substitute the mass and acceleration:
$8\ \text{kg} \times 3\ \text{m/s}^2$
Calculate the force:
$24\ \text{N}$

The resultant force is 24 N.

Common Mistake

Confusing mass and force

Mass is measured in kg. Force is measured in N. Weight is a force, so weight must be measured in N, not kg.

Newton/kilogram, N/kg: unit of gravitational field strength

Gravitational field strength tells you how much gravitational force acts on each kilogram of mass. It is measured in newtons per kilogram, N/kg.

The equation is:

weight = mass × gravitational field strength

\times g

where:

$W$ is weight in N
$m$ is mass in kg
$g$ is gravitational field strength in N/kg

Definition

Gravitational field strength

Gravitational field strength is the force of gravity per kilogram of mass at a point. Its unit is N/kg.

On Earth, gravitational field strength is about 10 N/kg at IGCSE level. That means each kilogram of mass experiences about 10 N of weight.

Example

Calculating gravitational field strength

An astronaut has a mass of 70 kg. On a planet, their weight is 280 N. Calculate the planet’s gravitational field strength.

Rearrange the equation $\times g$ to make $g$ the subject:
$\frac{W}{m}$
Substitute the values with units:
$\frac{280\ \text{N}}{70\ \text{kg}}$
Calculate the gravitational field strength:
$4\ \text{N/kg}$

The planet’s gravitational field strength is 4 N/kg.

Key Idea

N/kg and m/s² are linked

Choosing the correct unit

A good way to choose a unit is to ask: “What type of quantity is this?”

If the question asks for...	Use this unit
mass	kg
distance, height or radius	m
time	s
speed or velocity	m/s
acceleration	m/s²
force, weight or thrust	N
gravitational field strength	N/kg

Example

Selecting units from quantities

A question gives the mass of a probe, the force on it and the time taken for a signal to arrive. State suitable units for each quantity.

Mass is the amount of matter, so its unit is kg.
Force is a push or pull, so its unit is N.
Time is a duration, so its unit is s.

The suitable units are kg, N and s.

Unit discipline in calculations

Tip

A quick unit check

If you divide metres by seconds, the unit must be m/s. If you multiply kilograms by m/s², the unit must be N.

Common Mistake

Convert before calculating

If an equation needs SI units, convert first. For example, use metres instead of kilometres and seconds instead of minutes unless the question clearly allows another unit.

Exam technique

In the exam

Identify the quantity being asked for first, then choose the matching unit: kg, m, s, m/s, m/s², N or N/kg.
In calculations, write units in your substitution line so you are less likely to mix up mass, weight, speed or acceleration.
Check whether any values need converting, especially km to m or minutes to seconds.

Self review

Check yourself

What is the difference between the units kg and N?
Why is acceleration measured in m/s² rather than m/s?
A planet has gravitational field strength 6 N/kg. What does that mean in words?

What you'll learn

Why units matter

SI units

The main units in 8.1

Kilogram, kg: unit of mass

Metre, m: unit of distance

Second, s: unit of time

Metre/second, m/s: unit of speed and velocity

Metre/second squared, m/s²: unit of acceleration

Newton, N: unit of force

Newton/kilogram, N/kg: unit of gravitational field strength

Choosing the correct unit

Unit discipline in calculations

Review Units by teaching Genie

Remember key concepts with flashcards

Units

What you'll learn

Why units matter

SI units

The main units in 8.1

Kilogram, kg: unit of mass

Metre, m: unit of distance

Second, s: unit of time

Metre/second, m/s: unit of speed and velocity

Metre/second squared, m/s²: unit of acceleration

Newton, N: unit of force

Newton/kilogram, N/kg: unit of gravitational field strength

Choosing the correct unit

Unit discipline in calculations

Review Units by teaching Genie

Remember key concepts with flashcards

Units

What you'll learn

Why units matter

SI units

The main units in 8.1

Kilogram, kg: unit of mass

Metre, m: unit of distance

Second, s: unit of time

Metre/second, m/s: unit of speed and velocity

Metre/second squared, m/s²: unit of acceleration

Newton, N: unit of force

Newton/kilogram, N/kg: unit of gravitational field strength

Choosing the correct unit

Unit discipline in calculations

Review Units by teaching Genie

Remember key concepts with flashcards

Units Revision Guide

Units

What you'll learn

Why units matter

SI units

The main units in 8.1

Kilogram, kg: unit of mass

Metre, m: unit of distance

Second, s: unit of time

Metre/second, m/s: unit of speed and velocity

Metre/second squared, m/s²: unit of acceleration

Newton, N: unit of force

Newton/kilogram, N/kg: unit of gravitational field strength

Choosing the correct unit

Unit discipline in calculations

Review Units by teaching Genie

Remember key concepts with flashcards

Units Revision Guide