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Elastic potential energy calculator

GCSEA-level Energy and power

The energy stored in a stretched or compressed spring.

E_e = ½ k e²

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_eElastic potential energy to find 0.640 J

kSpring constant

eExtension

Significant figures

Working

Write the equation
E_e = ½ k e²
Substitute the values
E_e = ½ × 200 × 0.08²
Calculate
E_e = 0.64 J
Give the answer to 3 significant figures
E_e = 0.640 J

Worked example

Find Ee, the elastic potential energy. Given: spring constant k = 200 N/m; extension e = 0.0800 m.

Write the equation
E_e = ½ k e²
Substitute the values
E_e = ½ × 200 × 0.08²
Calculate
E_e = 0.64 J
Give the answer to 3 significant figures
E_e = 0.640 J

Symbols and units

Symbol	Quantity	SI unit
E_e	Elastic potential energy	J
k	Spring constant	N/m
e	Extension	m

Elastic potential energy: rearranged

To find elastic potential energy: E_e = ½ k e²
To find spring constant: k = 2E_e / e²
To find extension: e = √(2E_e / k)

Exam tip

Square the extension before you multiply. Extension in metres, not centimetres.

Common questions

What is the formula for elastic potential energy?

The equation is Ee = ½ k e², where Ee is the elastic potential energy (J); k is the spring constant (N/m); e is the extension (m).

What units should I use for elastic potential energy?

In SI units: elastic potential energy in J, spring constant in N/m, extension in m. The calculator also accepts common alternatives such as kilometres, grams or minutes, and converts them for you.

How do I rearrange Ee = ½ k e²?

Rearranging gives these forms: to find elastic potential energy: Ee = ½ k e². to find spring constant: k = 2Ee / e². to find extension: e = √(2Ee / k).

Practise elastic potential 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.

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