Hooke'S Law Calculator
Estimate force for a small displacement of an approximately linear spring. A negative displacement gives a negative signed applied force under the chosen axis.
How the result changes
Only spring stiffness changes; all other inputs stay at your current values. The line illustrates the formula across the shown range. This is not a forecast of real-world outcomes.
About this calculation
Hooke'S Law Calculator calculates force magnitude with sign convention from spring stiffness, extension from equilibrium. Estimate force for a small displacement of an approximately linear spring. The main answer uses N and follows the specific assumptions explained below.
Formula
Applied force along the extension direction = spring stiffness × displacement from equilibrium.
Worked example
With Spring stiffness: 200 N/m, Extension from equilibrium: 0.05 m, force magnitude with sign convention is 10 N.
Inputs and calculation
Measure displacement from the spring's unloaded reference in meters. Multiply by stiffness in newtons per meter to find the external force required for a static extension or compression. The displayed relationship is Applied force along the extension direction = spring stiffness × displacement from equilibrium. Keep the fields' displayed units attached when reproducing this relationship by hand.
Worked numerical example
For example, enter spring stiffness 200 N/m, extension from equilibrium 0.05 m. Those inputs produce force magnitude with sign convention of 10 N.
Holding the other example values fixed, change spring stiffness from 200 to 220 N/m. The main output becomes 11 N. This comparison isolates the effect of that one input.
How to read and use the result
A negative displacement gives a negative signed applied force under the chosen axis. The spring's restoring force points in the opposite direction and is −kx. Estimate force for a small displacement of an approximately linear spring.
Practical context
A spring stiffness of 200 newtons per meter and a 0.05-meter extension require a 10-newton applied force at static equilibrium. Doubling extension within the linear range doubles force. If displacement is negative because the spring is compressed along the chosen axis, the signed applied force is negative; the restoring force has the opposite sign.
Assumptions and scope
The spring remains in its linear elastic range and stiffness is approximately constant. Preload, friction, damping and dynamic acceleration are excluded. Replace the example defaults with measured inputs for your situation and account separately for factors outside these fields.
Checks and common mistakes
Do not use centimeters as meters; 5 cm is 0.05 m. A spring stretched beyond its elastic limit will not necessarily obey the same k value.
Common questions
What should I verify before using the Hooke'S Law Calculator result?
A real spring may have an initial preload or stop behaving linearly at large displacement, so measuring several force-extension pairs is a useful check. Stiffness may be measured experimentally as the slope of force versus displacement. A single force-extension pair can give an approximate k only if the line passes near the unloaded origin; a preloaded spring needs its preload modeled separately.
Inputs
- Spring stiffness (N/m)
- Extension from equilibrium (m)