Spring Rate Calculator
The spring rate (stiffness) of a helical coil spring depends on four factors: wire diameter, mean coil diameter, number of active coils, and the wire material's shear modulus. The formula k = Gd^4 / (8D^3Na) lets you predict the force per unit deflection before building a single prototype. This calculator handles common spring materials and gives results in both metric and imperial units.
The fundamental formula for a helical compression or extension spring:
k = G x d^4 / (8 x D^3 x Na)
Where:
- k = spring rate (N/mm or lb/in)
- G = shear modulus of the wire material
- d = wire diameter
- D = mean coil diameter (OD minus one wire diameter)
- Na = number of active coils
Notice that wire diameter has a fourth-power effect: doubling wire diameter makes the spring 16 times stiffer. Coil diameter has a cube effect in the denominator: doubling coil diameter makes the spring 8 times softer.
The spring index C = D/d is an important design parameter:
- C < 4: Very stiff, hard to manufacture, high stress concentration
- C = 4-12: Ideal manufacturing range
- C > 12: Prone to tangling and buckling, harder to control tolerances
Active coils are the coils that actually deflect. Closed and ground ends are inactive. For closed ends, subtract 2 from total coils. For closed and ground ends (most common), also subtract 2.