Spring Rate Calculator

Find a compression spring’s rate from its dimensions and wire, or from a quick force and deflection test.

Calculate Spring Rate From
How far you compress it.
Fractions and decimals both work.
Lb. per Inch
Metric rate
Active coils
Spring index
Solid height
Force at deflection
Shear stress
Mean Diameter

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SpringWire × ODCoilsLb./In.N/mmRemove

How to Calculate Spring Rate

Spring rate (stiffness) is the force it takes to compress a spring one unit of length. For a helical compression spring it comes from the wire size, coil size, number of working coils and the wire's shear modulus G.

k (lb/in) = G × d⁴ ÷ (8 × D³ × Na)

d is the wire diameter, D the mean coil diameter (outside diameter minus the wire diameter), and Na the active coils: total coils minus 2 for closed ends, minus 1 for open ground ends, and all of them for plain open ends. Measured from a test, rate is simply force ÷ deflection (Hooke's law).

Shear stress = 8 × F × D × Kw ÷ (π × d³)   Kw = (4C − 1) ÷ (4C − 4) + 0.615 ÷ C   C = D ÷ d

Worked Example

Shear Modulus of Spring Wire

MaterialG (Million PSI)

From Gardner Spring's table of material properties. G varies a little with heat treatment and cold work.

Tips

A spring index (C) between about 4 and 12 is easiest to make; below 4 is hard to coil and above 12 tends to tangle and buckle. Check that the spring doesn't go solid before your working deflection, and compare the shear stress to the wire maker's allowable stress for your wire size.