Spring Rate Calculator

This professional spring rate calculator helps mechanical engineers, suspension tuners, and makers quickly compute coil spring stiffness. Calculate spring rate from material and geometry, derive it from load and deflection, or estimate wheel rate using motion ratio and installation angle—with accessible, mobile‑first UX.

Interactive Calculator

Choose calculator mode
Create a shareable permalink of your current inputs.
For round‑wire helical springs, rate depends on the shear modulus G. Values vary by alloy and heat treatment.
G = 79.3 GPa
mm
Measure the wire thickness.
Enter one: Outer Do, Mean Dm, or Inner Di. The calculator converts to mean diameter using Dm = Do − d = Di + d.
mm
Count only the coils that deflect under load. End coils may be inactive.

Results

  • Spring rate (N/mm) —
  • Spring rate (N/m) —
  • Spring rate (lbf/in) —

Data Source and Methodology

Authoritative reference: Shigley’s Mechanical Engineering Design, 11th Edition (McGraw‑Hill, 2020), Section on Helical Springs; and Roark’s Formulas for Stress and Strain, 8th Edition (McGraw‑Hill, 2012), Chapter on Springs. Direct resources: Shigley 11e, Roark’s 8e.

All calculations are strictly based on the formulas and data provided by this source.

The Formula Explained

Coil spring (round wire) rate:

$$k \;=\; \frac{G\,d^{4}}{8\,D_m^{3}\,N_a}$$

Mean diameter relationships:

$$D_m \;=\; D_o - d \;=\; D_i + d$$

From load and deflection:

$$k \;=\; \frac{F}{\Delta}$$

Wheel rate (using MR = spring travel / wheel travel, angle θ to wheel motion):

$$k_w \;=\; k_s \,\big(\mathrm{MR}\big)^{2}\,\cos^{2}\!\theta$$

Glossary of Variables

k
Spring rate (stiffness) of the coil spring.
G
Shear modulus of the spring material (Pa, psi).
d
Wire diameter.
Dm, Do, Di
Mean, outer, and inner coil diameters respectively.
Na
Number of active coils that deflect under load.
F
Applied force per spring.
Δ
Deflection under load.
MR
Motion ratio = spring travel ÷ wheel travel.
θ
Installation angle between spring axis and wheel motion direction.
C
Spring index, C = Dm/d (good practice typically 4–12).

How It Works: A Step‑by‑Step Example

Goal: Compute the spring rate of a steel coil spring.

  1. Choose Metric (SI) and Material = Music Wire steel (G = 79.3 GPa).
  2. Enter wire diameter d = 10 mm; select “Outer Do” and set Do = 70 mm; set active coils Na = 8.
  3. Mean diameter Dm = Do − d = 60 mm.
  4. Convert to meters: d = 0.010 m, Dm = 0.060 m; G = 79.3×109 Pa.
  5. Apply the formula: k = G d⁴ / (8 Dm³ Na) ≈ 15.1 N/mm ≈ 86.2 lbf/in.

Frequently Asked Questions (FAQ)

How do I pick the correct number of active coils?

Count only the coils that deflect under load. Ground or closed ends may be inactive. Manufacturer drawings often specify Na.

Is mean diameter different from outer diameter?

Yes. Mean diameter Dm is measured to the wire centerline. Dm = Do − d = Di + d.

What units should I use?

Choose Metric (SI) or Imperial. The calculator outputs N/mm, N/m, and lbf/in simultaneously regardless of the chosen input system.

What is a good spring index C?

Values between 4 and 12 are commonly recommended for manufacturability and performance. Very low or high C can increase stress or instability.

How does installation angle affect wheel rate?

Only the component of stiffness along the wheel travel contributes: kw = ks·MR²·cos²θ. Larger angles reduce effective wheel rate.

Does this account for end conditions and preload?

Rate is independent of preload. End conditions affect active coil count; ensure Na reflects your spring’s ends.

Is this suitable for extension springs?

The rate equation is the same for round‑wire helical springs, but design factors (hooks, initial tension) are not included.

Tool developed by Ugo Candido. Content verified by the CalcDomain Mechanical Review Team. Last reviewed for accuracy on: September 15, 2025.