All solvers

    Spring Force Calculator (F = ke)

    GCSE PhysicsAQAEdexcelOCRFoundation & Higher

    Find force, spring constant or extension using F = k × e, often called Hooke's law. Enter centimetres or millimetres and the solver converts to metres.

    Quick answer

    Force = spring constant × extension. Use k in N/m and extension in metres to get newtons. For example, a 50 N/m spring stretched by 6 cm (0.06 m) needs 50 × 0.06 = 3.0 N. It works up to the limit of proportionality.

    By Engr. Mehmood Kakar · Updated

    F = k × e
    Find:

    Extension = stretched length − original length.

    Simulation

    Hooke’s law and its limit

    Change the spring constant and the extension. The force grows in proportion to the extension, until the spring passes its limit of proportionality.

    40 N/m
    0.25 m

    F = ke only works up to the limit of proportionality. Beyond it the graph curves and the spring may not return to its original length.

    Put these numbers in the calculator above

    How to use F = ke

    When you stretch a spring, the force needed depends on how stiff the spring is and how far you stretch it:

    force = spring constant × extension

    • F is force in newtons (N)
    • k is the spring constant in newtons per metre (N/m)
    • e is extension in metres (m)

    A spring with k = 50 N/m stretched by 6 cm (0.06 m) needs a force of 50 × 0.06 = 3.0 N. A stiffer spring has a bigger spring constant.

    Extension is how much longer the spring gets, not its total length. If a 12.0 cm spring stretches to 18.0 cm, the extension is 6.0 cm.

    The equation only works up to the limit of proportionality. Below that limit, force and extension are directly proportional, so the force–extension graph is a straight line through the origin. Beyond it, the line curves and F = ke no longer applies. The same equation also works for compression.

    Common mistakes that cost marks

    1. Using the total length instead of the extension. Extension = stretched length − original length.
    2. Leaving extension in centimetres. 6 cm is 0.06 m. Divide by 100.
    3. Using F = ke past the limit of proportionality. Beyond that point force and extension are no longer proportional.
    4. Mixing up F = ke and Ee = ½ke². The first gives force in newtons; the second gives stored energy in joules.

    Practice questions

    Try each one on paper first, then reveal the worked answer.

    Q1A spring is 12.0 cm long. A force stretches it to 18.0 cm. The spring constant is 50 N/m. Calculate the force.[3 marks]
    1. Extension: e = 18.0 − 12.0 = 6.0 cm = 0.060 m
    2. F = k × e
    3. F = 50 × 0.060
    4. F = 3.0 N
    Q2A force of 12 N stretches a spring by 8.0 cm. Calculate the spring constant.[3 marks]
    1. Rearrange: k = F ÷ e
    2. Convert: e = 8.0 ÷ 100 = 0.080 m
    3. k = 12 ÷ 0.080
    4. k = 150 N/m
    Q3A spring has a spring constant of 90 N/m. Calculate its extension when a 4.5 N force is applied.[2 marks]
    1. Rearrange: e = F ÷ k
    2. e = 4.5 ÷ 90
    3. e = 0.050 m (5.0 cm)

    Endless practice

    A new question every time, marked instantly. Work it out on paper, then type your answer.

    Loading a question…

    Frequently asked questions

    What is the equation for spring force?

    Force = spring constant × extension (F = ke). Force is in newtons (N), spring constant in N/m and extension in metres (m).

    What is the limit of proportionality?

    The point beyond which force and extension stop being directly proportional. Past it, the force–extension graph curves and F = ke no longer applies.

    What does the spring constant tell you?

    How stiff the spring is. A bigger spring constant means more force is needed for each metre of extension.

    How do I find the spring constant from a graph?

    On a force–extension graph, the spring constant is the gradient of the straight-line section: force ÷ extension.