Paritian

Physics

Hooke's Law Spring Calculator

Force in a spring at a given extension, the energy stored, the sag under a mass and the natural frequency.

Results

Force 10.0000 N
Energy 0.20000 J
Extension 78.453 mm
Frequency 1.7794 Hz

What this tool does

The law holds only while the spring returns to its original length. Stretch it past the elastic limit and it takes a permanent set, after which none of these numbers apply. The natural frequency is the same relationship seen from the other side: it is what decides whether a suspension feels firm or wallowy.

Formula

F = k × x ; E = ½ k x²

Variables

SymbolMeaningUnit
kSpring constantN/m
xExtensionmm
mMasskg
FForceN
ENEnergyJ
XMExtensionmm
FQFrequencyHz

Worked example

  • Spring constant250 N/m
  • Extension40 mm
  • Mass2 kg
  • Force10.0000 N
  • Energy0.20000 J
  • Extension78.453 mm
  • Frequency1.7794 Hz

Limitations

  • The formula assumes ideal conditions: no friction losses, no air resistance and no efficiency losses unless you enter them.
  • For work that must comply with a standard or be signed off, check the result against the applicable code and have it reviewed by a qualified engineer.