Your Equation

Library / Tools / Physics equation calculator / Hooke’s law

Hooke’s law calculator

GCSEA-level Forces

The force needed to stretch or compress a spring is proportional to its extension, up to the limit of proportionality.

F = k e

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

18.0 N

Working

  1. Write the equation
    F = k e
  2. Substitute the values
    F = 120 × 0.15
  3. Calculate
    F = 18 N
  4. Give the answer to 3 significant figures
    F = 18.0 N

Worked example

Find F, the force. Given: spring constant k = 120 N/m; extension e = 0.150 m.

  1. Write the equation
    F = k e
  2. Substitute the values
    F = 120 × 0.15
  3. Calculate
    F = 18 N
  4. Give the answer to 3 significant figures
    F = 18.0 N

Symbols and units

SymbolQuantitySI unit
FForceN
kSpring constantN/m
eExtensionm

Hooke’s law: rearranged

  • To find force: F = k e
  • To find spring constant: k = F / e
  • To find extension: e = F / k

Exam tip

e is the extension from the natural length, not the total length of the spring.

Common questions

What is the formula for hooke’s law?

The equation is F = k e, where F is the force (N); k is the spring constant (N/m); e is the extension (m).

What units should I use for hooke’s law?

In SI units: force in N, 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 F = k e?

Rearranging gives these forms: to find force: F = k e. to find spring constant: k = F / e. to find extension: e = F / k.

Practise hooke’s law questions

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

Related

Read the full explanation on the Hooke’s law formula page. More forces equations: Newton’s second law, Weight, Moment of a force, Pressure, Pressure in a liquid, Density, Horizontal component of a force, Vertical component of a force. See the full list on the physics equation calculator page.