Library / Tools / Physics equation calculator / Kinetic energy

Kinetic energy calculator

GCSEA-level Energy and power

The energy an object has because it is moving.

E_k = ½ m v²

This free calculator is for GCSE and A-level physics. Choose the quantity you want to find, enter the other values with their units, and it shows the working in the layout used in exams, with the answer to the number of significant figures you choose. The values shown are an example. Change them to your own.

Quantity to find

E_kKinetic energy to find 16.0 J

mMass

vSpeed

Significant figures

Working

Write the equation
E_k = ½ m v²
Substitute the values
E_k = ½ × 2 × 4²
Calculate
E_k = 16 J
Give the answer to 3 significant figures
E_k = 16.0 J

Worked example

Find Ek, the kinetic energy. Given: mass m = 2.00 kg; speed v = 4.00 m/s.

Write the equation
E_k = ½ m v²
Substitute the values
E_k = ½ × 2 × 4²
Calculate
E_k = 16 J
Give the answer to 3 significant figures
E_k = 16.0 J

Symbols and units

Symbol	Quantity	SI unit
E_k	Kinetic energy	J
m	Mass	kg
v	Speed	m/s

Kinetic energy: rearranged

To find kinetic energy: E_k = ½ m v²
To find mass: m = 2E_k / v²
To find speed: v = √(2E_k / m)

Exam tip

Square only the speed, not the mass or the ½. Doubling the speed makes the kinetic energy four times bigger.

Common questions

What is the formula for kinetic energy?

The equation is Ek = ½ m v², where Ek is the kinetic energy (J); m is the mass (kg); v is the speed (m/s).

What units should I use for kinetic energy?

In SI units: kinetic energy in J, mass in kg, speed in m/s. The calculator also accepts common alternatives such as kilometres, grams or minutes, and converts them for you.

How do I rearrange Ek = ½ m v²?

Rearranging gives these forms: to find kinetic energy: Ek = ½ m v². to find mass: m = 2Ek / v². to find speed: v = √(2Ek / m).

Practise kinetic energy questions

Include unit conversions (km, g, minutes…)

Press the button for a question with random numbers. Work it out on paper first, then type your answer.

More energy and power equations: Work done, Work done by an angled force, Elastic potential energy, Power from force and speed, Gravitational potential energy, Power, Energy transferred, Efficiency. See the full list on the physics equation calculator page.