Spring Potential Energy Calculator

This calculator finds the elastic potential energy stored in a spring system, including the case of two springs combined in series or in parallel. When a spring is stretched or compressed, it stores energy that is released when it returns to its natural length, and the amount is one half of the spring constant times the displacement squared. Real mechanisms often use more than one spring, and how they are connected changes the effective stiffness: springs in parallel, side by side, add their constants and so are stiffer, while springs in series, end to end, combine like resistors in parallel and are softer than either alone. Getting the effective spring constant right is essential before working out the stored energy or the force. This calculator handles both arrangements. You enter the two spring constants, choose whether they are in series or parallel, and enter the displacement from the natural length, and the calculator returns the energy stored, the effective spring constant of the combination, the restoring force at that displacement, and the arrangement. The results update as you type. Use it for physics study, for designing spring systems, or to understand how springs combine. The effective constant for parallel springs is the sum of the two, while for series springs it is the reciprocal of the sum of the reciprocals, the same rule as parallel resistors. The stored energy is then one half of the effective constant times the displacement squared, and the force is the effective constant times the displacement, by Hooke's law. Because energy depends on the square of the displacement, stretching twice as far stores four times the energy. To use a single spring, set the second constant very high in series, or to zero in parallel, so it does not affect the result; or simply read the energy for one spring from its constant directly. The calculation assumes the springs stay within their elastic limit.

Energy = ½ x effective k x displacement². Parallel: k = k1 + k2 (stiffer). Series: k = 1/(1/k1 + 1/k2) (softer). Force = effective k x displacement. Within the elastic limit.