What is spring rate (k)?

Spring rate, also called spring stiffness or spring constant, is the force required to compress or extend a spring by one unit of length (N/mm or lbf/in). A stiffer spring has a higher k value. For torsion springs k is expressed as torque per unit angle (N·mm/deg).

What is the formula used for compression and extension springs?

k = (G × d⁴) / (8 × D³ × Na), where G is the shear modulus, d is the wire diameter, D is the mean coil diameter, and Na is the number of active coils. This is the standard helical spring rate formula per SAE and Shigley's.

What is the formula for torsion springs?

k = (E × d⁴) / (10.8 × D × Na) in consistent units, where E is the elastic modulus (Young's modulus, not shear modulus). The result is in torque-per-radian and is converted to N·mm/deg or in·lbf/deg.

What shear modulus should I use for steel springs?

Standard carbon steel music wire uses G ≈ 79,000 MPa (11,500,000 psi). Stainless steel (302/304) uses G ≈ 69,000 MPa. Chrome-silicon and chrome-vanadium alloy steels use G ≈ 77,500–79,300 MPa.

What is the Wahl correction factor?

The Wahl correction factor (Kw) accounts for stress concentration due to wire curvature and direct shear in helical springs. It is calculated as Kw = (4C − 1)/(4C − 4) + 0.615/C, where C = D/d is the spring index. It is used to determine the actual maximum shear stress in the wire.

How do I find the mean coil diameter?

Mean coil diameter (D) = Outer diameter − wire diameter, or Inner diameter + wire diameter. It is measured from the centerline of the wire on one side of the coil to the centerline of the wire on the opposite side.

Spring Rate Calculator

Name: Spring Rate Calculator
Availability: InStock
Author: Nham Vu

Calculate spring rate (k) for compression, extension, or torsion springs by entering wire diameter, coil diameter, active coils, and shear modulus.

Spring Parameters

Spring Type

Unit System

Wire Diameter (d) — mm

Mean Coil Diameter (D) — mm

Number of Active Coils (Na)

Shear Modulus (G) — MPa

Steel: 79,000 MPa · Stainless: 69,000 MPa · Copper: 26,500 MPa

Quick Presets

Enter parameters on the left and click
Calculate Spring Rate

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Summary

Calculate spring rate (k) for compression, extension, or torsion springs by entering wire diameter, coil diameter, active coils, and shear modulus.

How it works

Select the spring type: Compression / Extension or Torsion.
Enter the wire diameter (d) in your preferred unit.
Enter the mean coil diameter (D) — measured from center of wire to center of wire across the coil.
Enter the number of active coils (Na) — for compression springs this excludes closed end coils.
Enter the shear modulus (G) — common values are 79,000 MPa for steel or 26,500 MPa for copper alloys.
The calculator instantly returns spring rate (k), spring index (C), and Wahl correction factor (Kw).

Use cases

Validating mechanical spring designs for automotive suspension systems.
Calculating spring stiffness for industrial machinery and tooling.
Selecting the correct replacement spring by matching stiffness values.
Designing torsion springs for door hinges, clips, and return mechanisms.
Checking whether a spring will buckle or need a guide rod.
Iterating wire and coil diameter ratios to hit a target spring rate.
Academic coursework in mechanical engineering and machine design.
Quick field verification of spring specifications on-site.

Frequently Asked Questions

Last updated: 2026-06-13 · Reviewed by Nham Vu