TAHA Engineering Toolsby TAHA Knowledge Lab

Mechanical Engineering

Spring Rate Calculator (Hooke’s Law)

Spring rate, force or deflection using Hooke’s law — plus stored energy.

Inputs

Calculate from
Spring at free length above, and the same spring compressed by force F and deflection x below.Free lengthFx
Top: spring at its free length. Bottom: a force F compresses it by deflection x. Spring rate k = F ÷ x. Diagram not to scale.

Result

Spring rate
10
Energy stored
0.5

The spring needs 100 N to deflect 10 mm, so its rate is 10 N/mm. It stores 0.5 J.

Educational estimate — check the assumptions below.

About this calculator

The spring rate (stiffness, spring constant) is the force needed per unit of deflection. Within its working range a spring is linear: twice the force gives twice the deflection. Use this to check a spring from a test (force and deflection), or to find the force a known spring will give at a set compression.

Formula

F = k × x    E = ½kx²

F = force (N), k = spring rate (N/m), x = deflection (m), E = elastic energy stored (J).

Worked example

  • A spring compresses 10 mm under 100 N: k = 100 ÷ 10 = 10 N/mm; energy stored = ½ × 10 000 N/m × 0.01² = 0.5 J.
  • A 5 N/mm spring compressed 20 mm gives 100 N.
  • Imperial: 50 lbf over 2 in → 25 lbf/in (4.378 N/mm).

Assumptions and limitations

  • Linear spring within its elastic range. Do not exceed the maximum deflection or solid height given by the manufacturer.
  • Designing a spring from wire size, coil diameter and number of coils needs material data and is not covered here.

References

  • Hooke’s law and elastic strain energy, as given in mechanics texts.