How to Use Hooke's Law (F = kx): Force, Spring Constant & Stretch

Use Hooke's law F = kx to find spring force, constant k, or displacement x. Worked examples, unit traps, and a free Hooke's law calculator.

What Hooke's Law Asks

Hooke's law models an ideal spring: the restoring force is proportional to how far the spring is stretched or compressed from its unstretched length. Intro physics writes that as F = kx.

k is the spring constant (stiffness). A larger k means a stiffer spring. x is the displacement from equilibrium, not the full length of the coil.

If you already have two of F, k, and x and only need a checked third value, open the free Hooke's law calculator first, then return here for units and elastic-limit traps.

The Formula

  • F = kx — force magnitude in newtons.
  • k = F / x — spring constant in N/m.
  • x = F / k — stretch or compression in meters.

    • Direction: the spring force opposes the displacement. Many answers report the magnitude from F = kx and state the direction in words.

    Units

  • F → N.
  • k → N/m.
  • x → m (convert cm first: divide by 100).

    • Worked Examples

    Example 1: find the force

    k = 200 N/m, x = 0.15 m. F = kx = 30 N.

    Example 2: find k

    F = 40 N, x = 0.080 m. k = F / x = 500 N/m. Using 8 cm as 8 instead of 0.080 breaks the answer.

    Example 3: find the stretch

    F = 12 N, k = 150 N/m. x = F / k = 0.080 m = 8.0 cm.

    Elastic Limit

    Hooke's law is linear only inside the elastic range. Past the elastic limit the spring permanently deforms and F is no longer proportional to x. Use F = kx when the problem calls the spring ideal or stays within that range.

    A mass on a spring with F = −kx is simple harmonic motion with period T = 2π√(m/k). Compare with the simple harmonic motion calculator and the pendulum period T = 2π√(L/g).

    Common Mistakes

  • Leaving x in centimeters while k is in N/m.
  • Using total spring length instead of stretch from the unstretched length.
  • Mixing mass m into F = kx as if it were the spring constant.
  • Applying F = kx after a plastic stretch.

    • Check It on the Calculator

    Hooke's law calculator.

    Simple harmonic motion calculator.

    Simple pendulum calculator.

    Force calculator.

    Learn F = kx and check every spring homework number.

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