Spring rate calculator
Calculate the stiffness (spring rate) of a round-wire helical compression spring from its geometry and material.
How it is calculated
k = G × d⁴ ÷ (8 × D³ × N), where G is the shear modulus, d the wire diameter, D the mean coil diameter and N the number of active coils.
Worked example
G = 79,300 MPa, d = 2 mm, D = 16 mm, N = 10: k = 79,300 × 16 ÷ (8 × 4096 × 10) = 3.87 N/mm.
Steps
- Enter the shear modulus of the wire material.
- Enter wire diameter and mean coil diameter (outside diameter minus one wire diameter).
- Enter the active coils, then read the rate.
Frequently asked questions
What is the mean coil diameter?
The average of the outside and inside coil diameters, which equals the outside diameter minus the wire diameter.
What spring index is good?
A spring index C = D ÷ d between 4 and 12 is typical. Very small indexes are hard to wind; large ones are unstable.
Does this include end coils?
No. Enter only the active coils. Closed and ground ends add non-active coils.
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References
k = G d⁴ ÷ (8 D³ N) from Shigley, Mechanical Engineering Design; SAE J157 and EN 13906 for spring design data.
Estimates for information only. Verify critical values with a qualified engineer or your supplier standards.