Spring Force Calculator

Hooke s law states that the elastic force is directly proportional to the deformation: F = k * x. The constant k (spring constant) describes the stiffness in newtons per metre (N/m). It holds within the elastic range, while the material returns to its original shape after the force is removed.

Use F = k * x, where k is the spring constant [N/m] and x is the deformation in metres. Example: for k = 500 N/m and x = 0.04 m the force is F = 500 * 0.04 = 20 N.

The spring constant k tells you how stiff the spring is — how many newtons are needed to stretch it by one metre. The larger k, the stiffer the spring. The unit is N/m; a spring with k = 1000 N/m is ten times stiffer than one with k = 100 N/m.

Use E = 0.5 * k * x^2. This is the work done deforming the spring and the energy stored in it. Example: k = 200 N/m, x = 0.1 m gives E = 0.5 * 200 * 0.01 = 1 J.

In E = 0.5 * k * x^2 the deformation is squared because the force grows linearly with x and energy is the area under the force-distance graph (a triangle). Doubling the deformation quadruples the energy rather than doubling it.

A hanging load stretches the spring until the elastic force balances the weight: k * x = m * g. Hence the static deflection x = m * g / k, with g = 9.81 m/s^2. A larger mass or a smaller k means a bigger extension.

For a mass m on a spring of stiffness k the harmonic oscillation period is T = 2 * PI * sqrt(m / k). Example: m = 1 kg, k = 100 N/m gives T = 2 * PI * sqrt(0.01) ~ 0.628 s. More mass lengthens the period; more stiffness shortens it.

The elastic force is a restoring force, always opposite to the deformation. Under compression (negative x) the force comes out negative in this sign convention. The calculator shows the signed numeric value; the direction always points back to equilibrium.

Hooke s law holds only within the material s elastic range. Beyond the elastic limit the force-deformation relation becomes non-linear, and past the yield point the material deforms permanently and does not return to its original shape.

Enter the spring constant k in N/m, the deformation x in metres (e.g. 0.05 m instead of 5 cm), and the optional mass m in kilograms. The force is returned in newtons (N), energy in joules (J), and the oscillation period in seconds (s).