Spring Rate Calculator
Helical spring rate from wire diameter, outside diameter, active coils and your shear modulus, with force, deflection and Wahl-corrected shear stress.
The stiffness a coil spring will have before it is wound, the load at a given compression, and the working stress to compare with the wire’s allowable — every formula stated.
Example: 2 mm wire, 20 mm OD, 8 active coils, G 79.3 GPa: mean diameter 18 mm, index 9, rate 3.40 N/mm. At 10 mm compression the load is 34.0 N and the corrected shear stress 226 MPa.
Fourth power of the wire,
cube of the coil.
The rate formula, the stress correction, why the shear modulus is yours to enter, and what a full spring design adds.
Spring rate
A helical spring deflects by twisting its wire. For round wire the rate is k = G d⁴ ÷ (8 D³ Nₐ): G the shear modulus of the wire, d the wire diameter, D the mean coil diameter (outside diameter minus one wire), Nₐ the number of active coils. The strong dependence on the wire — doubling d multiplies the rate by 16 — and the inverse cube of the coil diameter are why small dimensional changes matter so much, and why the table shows what changing the coil count alone does. Force is rate × deflection; the rate is the same in compression and extension (initial tension in extension springs is not modelled).
Stress and the Wahl factor
The wire carries a torsional shear stress 8FD ÷ (πd³), raised on the inside of the coil by curvature and direct shear. Wahl's factor K_w = (4C − 1)/(4C − 4) + 0.615/C, where C = D/d is the spring index, corrects for both; the page multiplies by it and reports the corrected stress. Whether that stress is acceptable depends on the wire material and diameter (tensile strength falls as wire gets thicker), on whether the load is static or cyclic, and on the design factor — comparisons the page leaves to you and your material data.
The shear modulus is material data
G differs between spring materials — carbon and alloy steels, stainless grades, phosphor bronze, beryllium copper, Inconel — and slightly with wire processing, so it is an input. The value shown at first is a labelled sample for a common steel spring wire from the cited textbook; use the figure from your wire specification. The spring index is flagged outside 4–12, the range the same source gives for springs that wind without difficulty and do not tangle, not as a rule.
Not covered
Solid height, free length, pitch, end types and their effect on active coils, buckling of slender compression springs, surge frequency, fatigue life and set removal are part of a full spring design and are outside this page. Nothing leaves the browser; the same four anonymous usage counts as the rest of the site apply.
SOURCES
- Budynas, R. G. & Nisbett, J. K., Shigley’s Mechanical Engineering Design, chapter 10 "Mechanical Springs" — spring rate, Wahl factor, spring index range 4–12
Last reviewed 19 September 2026. How results are checked: How we verify.