Quick Answer: How Do I Calculate Spring Rate?
Spring rate (k) is the force needed to compress a coil spring one unit of length, measured in lb/in or N/mm. For a round-wire compression spring it equals k = Gd⁴ / (8D³N), where G is the wire shear modulus, d the wire diameter, D the mean coil diameter and N the active coils. Wire diameter dominates: doubling d raises the rate about 16×.
This calculator computes spring rate, force at a target deflection, solid height and torsional shear stress for compression springs using the Wahl curvature-correction factor. Inputs include wire diameter, outside diameter, free length, active coils, end type and wire material (music wire, stainless, chrome silicon and more).
Design guidelines: spring index C = D/d should stay 4–12 (ideal 6–8) | music wire G ≈ 11.5 Mpsi | keep shear stress below 40% of tensile ultimate | never design operating deflection above 80% of travel to solid.
How Compression Springs Work
A compression spring pushes back when squeezed. The more you squeeze it the more force it pushes back with. The relationship is linear. Double the squeeze, double the force.
Spring Rate
Spring rate k tells you how much force per inch of compression. A 20 lb/in spring needs 20 pounds to compress it one inch. And 40 pounds to compress it two inches. Spring rate is the most important number in spring design.
What Affects Spring Rate?
Four things change spring rate. Wire diameter, coil diameter, number of coils, and material. Wire diameter matters most. Doubling wire diameter increases rate by sixteen times. Adding more coils makes the spring softer. Thicker wire makes it stiffer.
Pro tip: If your spring is too stiff, add more coils. If it is too soft, use bigger wire. Changing the coil diameter is a last resort because it also changes stress.
Spring Index
Spring index C equals the mean coil diameter divided by wire diameter. Good springs have C between 4 and 12. Index of 6 to 8 is ideal. Too low and the spring is hard to make. Too high and the spring buckles when compressed.
Shear Stress
When a spring compresses, the wire twists. This creates shear stress inside the wire. The Wahl factor accounts for the stress concentration on the inside of the coil. Keep stress below the material limit for a long spring life.
Solid Height
Solid height is the length when all coils touch. You cannot compress past this point. Design your spring so the operating deflection stays safely below solid. If you need more travel, use a longer free length or more coils.