Hooke's Law Calculator

This calculator applies Hooke's law to find the force in a stretched or compressed spring and the elastic potential energy it stores. Hooke's law is one of the first quantitative laws students meet in physics, and it is beautifully simple: the force a spring exerts is proportional to how far it has been stretched or compressed from its natural length. Written F equals k times x, the force equals the spring constant, a measure of stiffness, multiplied by the displacement. A stiff spring has a large spring constant and pushes back hard for a small stretch; a soft spring has a small one. The law explains the behaviour of springs, elastic materials, suspension systems, scales and countless mechanisms, and it holds as long as you do not stretch the material so far that it deforms permanently. This tool calculates both key quantities. You enter the spring constant in newtons per metre and the displacement in metres, and it returns the restoring force in newtons, the force the spring exerts to return to its natural length. It also computes the elastic potential energy stored in the spring, which is one half of the spring constant times the displacement squared, the energy that would be released if the spring were let go. The results update as you type, so you can see how the force grows in proportion to the stretch while the stored energy grows with its square. Use it for physics homework, for designing or understanding spring systems, or to build intuition for elasticity. The calculations use SI units and standard formulas, rounded for display, and assume the spring stays within its elastic limit.

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Force = spring constant x displacement. Elastic energy = half x spring constant x displacement squared. Valid within the elastic limit. Rounded for display.