Free · Dynamics calculators — Why things move ➡️

Linear Spring Restoring Force & Displacement

Calculate the signed restoring force of an ideal passive spring from its stiffness and change in length.

  • Formula & worked example
  • Private in your browser
  • No signup
Go to tool

Calculator inputs

Loading calculator…

How to use this calculator

  1. Enter the known values in the units shown. Results update as you type.
  2. Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
  3. Use the worked example to check the method. Reset restores the starting fields.

Private by default

Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.

Formula and method

A spring with stiffness 200 N/m extended by 0.1 m exerts a restoring force of −20 N along the extension axis. Compression by −0.1 m gives +20 N.

Restoring force = −kΔx; Δx = final length − equilibrium length

Worked example

Enter these known values and leave the other values blank.

Positive spring stiffness
200 N/m
Equilibrium spring length
0.5 m
Final spring length
0.6 m
Signed change in length
0.1 m
Spring restoring force
-20 N

Assumptions and limitations

  • Stiffness must be positive for this passive linear-spring model. Length inputs, when supplied, must be nonnegative.
  • The initial length represents the unstressed equilibrium length. A preloaded starting length does not define zero force unless its preload is handled separately.
  • A positive displacement means extension. The restoring-force sign is opposite displacement; it is the spring’s force, not the external force needed to hold it.
  • Use the relation only within the spring’s linear elastic range. The calculator does not assess allowable stress, buckling, coil contact or failure.

Common questions

Why is the restoring force negative during extension?

The positive axis follows extension, while the spring pulls toward equilibrium. The negative sign records this opposite direction.

Can I enter displacement directly?

Yes. Enter signed displacement and stiffness without supplying both lengths. The length relationship is useful when you know equilibrium and final length instead.

References

Bookify requires positive stiffness and nonnegative physical lengths for an ideal passive spring; displacement and restoring force remain signed.

Explore dynamics calculators — why things move ➡️ or browse all physics calculators.