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Hooke's Law Force Calculator

Enter the spring constant and displacement to find the restoring force and stored energy.

How it is calculated

Enter the spring constant k in newtons per metre (N/m) and the displacement x in centimetres, measured from the spring's natural length. The tool first converts the displacement to metres, x(m) = x(cm) / 100, then applies F = k × x for the restoring force in newtons and E = ½ × k × x² for the elastic energy in joules. The converted displacement is also displayed. The same numbers apply whether the spring is stretched or compressed, so enter the size of the change only; zero or negative inputs give no result. The law holds only within the spring's elastic range. A spring pushed past its limit stays deformed and this linear formula no longer describes it.

Worked example

A spring with k = 250 N/m is stretched 8 cm. First convert: 8 / 100 = 0.0800 m. Force: 250 × 0.08 = 20.00 N. Energy: ½ × 250 × 0.08² = 0.5 × 250 × 0.0064 = 0.8000 J. The tool shows a restoring force of 20.00 N, stored energy of 0.8000 J and a displacement of 0.0800 m. Doubling the stretch to 16 cm would double the force to 40 N but quadruple the energy to 3.2 J.

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Common mistakes

  • Entering the displacement in metres. The field expects centimetres, so 0.08 is read as 0.08 cm and the force comes out a hundred times too small; type 8 for 8 cm.
  • Giving k in N/cm or N/mm. The constant must be in N/m, so a spring rated 2.5 N/cm needs to be entered as 250.
  • Using the total length of the spring as x. Only the change from the natural, unloaded length counts.
  • Assuming energy is proportional to stretch. It grows with the square of x, so a double stretch stores four times the energy, not twice.
  • Applying the result beyond the elastic limit or to a spring with preload. A spring stretched too far no longer follows F = k·x, and a preloaded one needs the extension from its unloaded length, not from the mounted length.

Sources

About this calculator

Hooke's Law states that the force a spring exerts is directly proportional to how far it's stretched or compressed from its natural length: F = k·x, where k is the spring constant (stiffness, in N/m) and x is the displacement. This calculator applies that formula to find the restoring force, and also computes the elastic potential energy stored in the spring, ½·k·x², the work done to deform it.

Hooke's Law is a foundational relationship in introductory physics and mechanical engineering, underlying the design of everything from vehicle suspension springs and mattress coils to force sensors and mechanical scales. Engineers use it to select a spring constant that gives the right stiffness for an application, while physics students use it to connect force, energy, and simple harmonic motion — since a mass on a Hooke's-Law spring oscillates with a period set entirely by k and the mass.

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Comments (1)

  • Editorial team

    The tool takes one spring constant, so combine real springs first. Two identical springs side by side, both stretched together, act like one spring with double the constant; the same two springs joined end to end act like one with half the constant. Work out that single k, then enter it with the stretch in centimetres. Also remember the law only holds inside the elastic range. What kind of spring are you working with, and how do you get its constant?

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