How this calculation works
Normalize signed displacements relative to the unstressed spring. Force reverses with displacement, whereas stored energy depends on its square. Work compares endpoint energies rather than multiplying the final force by the whole travel.
Restoring force = −kx; stored energy = ½kx²; quasi-static external work = Ufinal − UinitialA worked example
For k = 200 N/m and a change from 0 to +0.1 m, the final restoring force is −20 N, stored energy is 1 J and quasi-static external work is +1 J. Returning to zero reverses the work sign.
Good to know
Ideal positive-stiffness linear spring within an assumed Hooke-law range. No preload, damping, plasticity, material limit, gravitational energy or attached-mass dynamics.
Reference: Reference: model, definitions and assumptions (opens in a new tab) ↗
The sign of force and the sign of energy answer different questions
For the default 200 N/m spring at +0.1 m, restoring force is −20 N and stored energy is 1 J. At −0.1 m, restoring force is +20 N but stored energy is still 1 J. Force points toward the unstressed reference; squaring displacement makes both equal-size deformations store the same energy.
The coordinate must be measured from the unstressed spring reference used by this model. A spring holding a mass vertically may already be stretched at its gravity-loaded equilibrium. Entering a displacement from that shifted equilibrium without accounting for the reference would describe a different energy question.
The kinetic energy calculator covers a separate motion term. Elastic spring energy depends on deformation relative to the unstressed reference, not automatically on an attached object’s speed.
Work uses the energy difference, not final force times travel
Moving quasi-statically from 0 to +0.1 m needs +1 J of external work in the ideal spring-only model. Multiplying the final 20 N force by the 0.1 m travel gives 2 J and overstates the answer because the force grows from zero throughout the change.
Starting at +0.2 m instead gives an initial 4 J. Ending at +0.1 m leaves 1 J, so external work is −3 J and the spring does +3 J. Moving between −0.1 m and +0.1 m leaves endpoint energy unchanged; nonzero travel does not by itself imply positive net work by a conservative spring.
Stiffness units can hide a factor of one thousand
A stiffness of 0.2 N/mm equals 200 N/m. With an entered final deformation of 100 mm, the result is the same −20 N and 1 J as the default SI example. Both displacement and stiffness units are converted before the force and energy are calculated.
The kinetic energy calculator addresses the motion of an attached object, which this page does not simulate. The gravitational potential energy calculator adds a different energy term when height changes. Here the work interpretation assumes a quasi-static deformation, no change in kinetic energy and no damping or other energy terms.
A few questions, answered
Can compression be entered as negative displacement?
Yes. Use one consistent signed coordinate relative to the unstressed reference. The restoring force reverses and stored energy remains non-negative.
Can external work be negative?
Yes. It is Ufinal − Uinitial under the stated quasi-static assumptions. The spring can return energy as deformation decreases.
Is this an oscillation or material-strength calculator?
No. It does not model mass motion, preload, damping, coil binding or an elastic limit.
Does equal initial and final stored energy mean no travel?
No. Equal-magnitude opposite displacements have equal stored energy while representing different positions.