Spring Rate Calculator — Helical Spring Stiffness
Design a helical spring by entering its wire diameter, mean coil diameter, number of active coils and material. The calculator gives the spring rate in N/mm, N/m, lb/in and kgf/mm, plus the spring index and Wahl stress-correction factor.
Spring material
mm
mm
coils
Stiffness of the spring — force required per mm of deflection
- 1
Wire diameter to the 4th power (d⁴)
2⁴ = 16 - 2
Mean coil diameter cubed (D³)
20³ = 8,000 - 3
Denominator: 8 × D³ × Na
8 × 8,000 × 10 = 640,000 - 4
Spring rate k = G × d⁴ ÷ (8 × D³ × Na)
81,500 × 16 ÷ 640,000 = 2.0375Units: (N/mm²) × mm⁴ ÷ mm³ = N/mm.
How does this calculator work?
Spring rate k = (G × d⁴) / (8 × D³ × Na) where G is shear modulus (N/mm²), d is wire diameter (mm), D is mean coil diameter (mm), and Na is active coils. Enter the four values (or pick a material preset) to get stiffness in N/mm, N/m, lb/in and kgf/mm, plus the spring index C = D/d.
Formula
How this is calculated
The spring rate of a helical coil spring is derived from torsion theory. When a load compresses or extends the spring, each coil is subjected to torsional stress. The resulting stiffness (k) depends on four physical parameters: the shear modulus G of the wire material (how resistant the material is to twisting), the wire diameter d raised to the fourth power (dominant influence), the mean coil diameter D cubed (larger coils are softer), and the number of active coils Na (more coils = softer spring). Doubling the wire diameter makes the spring 16× stiffer; doubling the coil diameter makes it 8× softer.
The shear modulus depends on the material: carbon steel (music wire) has G ≈ 81,500 N/mm², chrome-vanadium alloy steel ≈ 80,000 N/mm², stainless steel ≈ 69,000 N/mm², phosphor bronze ≈ 41,000 N/mm². The formula assumes the wire cross-section remains circular and uniform, and the spring is loaded axially with no buckling.
The spring index C = D/d is a dimensionless ratio (typically 4–12 for practical springs) that influences torsional stress distribution. The Wahl correction factor K_w accounts for curvature effects and direct shear near the inner coil surface, and is used in stress calculations. A spring index below 4 causes manufacturing difficulty; above 12 it can be prone to tangling. The result is provided in four common units for convenience.
Frequently asked questions
For a helical compression spring with squared-and-ground ends, two coils at each end are ground flat and do not deflect — they are inactive. Active coils = total coils − 2 (for both-ends-closed springs). Open-end springs have active coils = total coils − 1 or = total coils, depending on design. Tension springs typically have all coils active.
Spring rate scales with d⁴ — a fourth-power relationship. Increasing wire diameter by 10% raises the spring rate by (1.1)⁴ ≈ 46%. This extreme sensitivity means wire diameter is the primary lever for tuning spring stiffness during design.
Enter the shear modulus (G) of your wire material in N/mm² (= MPa). For metals it is often listed as the modulus of rigidity or torsional modulus in material datasheets. Common values: mild steel 80,000; beryllium copper 48,000; aluminium alloys 25,000–27,000 N/mm².
Also known as
TG we-Calculate Editorial Team. (2026). Spring Rate Calculator — Helical Spring Stiffness [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/spring-rate-calculator
TG we-Calculate Editorial Team. "Spring Rate Calculator — Helical Spring Stiffness." TG we-Calculate. 2026. https://we-calculate.com/calculator/spring-rate-calculator.
TG we-Calculate Editorial Team, "Spring Rate Calculator — Helical Spring Stiffness," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/spring-rate-calculator
@misc{wecalculate_spring_rate_calculator, title = {Spring Rate Calculator — Helical Spring Stiffness}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/spring-rate-calculator}}, year = {2026}, note = {TG we-Calculate} }
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