What is spring rate (stiffness)?

Spring rate k is the force required to compress the spring by one unit of length, calculated as k = (G × d⁴) / (8 × D³ × Na). A higher G or wire diameter increases stiffness; more active coils reduce it.

What is the spring index and why does it matter?

Spring index C = D / d. Values below 4 are difficult to manufacture; above 12 the spring may buckle or tangle. Indices between 6 and 9 are typical for good manufacturability.

What is the Wahl correction factor?

The Wahl factor Kw accounts for stress concentration at the inner coil surface and wire curvature. It amplifies the nominal shear stress and gives a more realistic peak stress value.

How is natural frequency calculated?

For the fixed-free approximation used here, natural frequency fn = (d / (4 × π × D² × Na)) × √(G / (2ρ)), where ρ is the material density. The spring should operate below one-third of its natural frequency to avoid resonance.

What does solid height mean?

Solid height Ls = Nt × d (total coils × wire diameter) is the length when all coils are fully compressed. The maximum working deflection must leave a small gap above solid height.

Which material should I select?

Music wire (ASTM A228) is the default for high-strength general applications. Hard-drawn wire is lower cost for static loads. Stainless 302 suits corrosive environments. Chrome-vanadium is preferred for elevated temperatures.

Spring Design Calculator

Compute spring rate, shear stress, deflection, and natural frequency for helical compression springs.

Spring Parameters

Material

Wire Diameter d (mm)

Mean Coil Diameter D (mm)

= outer diameter − wire diameter (approx.)

Active Coils Nₐ

Total Coils Nₜ (for solid height)

Typically active coils + 2 (closed ends)

Free Length L₀ (mm)

Applied Load F (N) — optional

Spring Properties

Spring Rate k

—

N/mm

Spring Index C

—

D / d

Solid Height Ls

—

Max Deflection (to solid)

—

Max Load (to solid)

—

Natural Frequency

—

Summary

This calculator covers all key parameters for helical compression spring design: spring rate, maximum shear stress with Wahl correction, deflection under load, solid height, and natural frequency. Enter wire and coil geometry plus material, and every output updates instantly in your browser — no data is sent to any server.

How it works

Enter the wire diameter (d) and mean coil diameter (D) of the spring.
Input the number of active coils and the free length.
Select the material to auto-fill shear modulus G and density.
Optionally enter an applied load to see deflection and shear stress at that load.
Results update instantly — spring rate, max load, natural frequency, and safety factor are all shown.

Use cases

Verify a commercial spring meets load and deflection requirements.
Size a new compression spring for a mechanical assembly.
Check shear stress against material yield strength during design.
Estimate natural frequency to avoid resonance in dynamic applications.
Compare spring stiffness across different wire gauges.
Validate spring design before ordering custom springs.

Frequently Asked Questions

Last updated: 2026-06-11 · Reviewed by Nham Vu

Spring Design Calculator

Spring Parameters

Spring Properties

At Applied Load

Design Notes

Summary

How it works

Use cases

Frequently Asked Questions

Spring Design Calculator

Use the Spring Design Calculator

Spring Parameters

Spring Properties

At Applied Load

Design Notes

Summary

How it works

Use cases

Frequently Asked Questions