# Spring Rate Calculator

URL: https://speedycalculator.com/calculators/physics/spring-rate/
Last updated: 2026-10-30

> The spring rate calculator finds the stiffness of a helical compression spring from its wire diameter, outer (or inner) diameter, number of active coils and shear modulus, with total coils, solid height and stress at a load.

## Inputs

- Wire diameter d (mm, cm, m, in, µm)
- Diameter given
- Diameter (mm, cm, m, in, µm)
- Active coils N_a
- Material
- End type
- Load (optional) (N, kN, MN, mN, lbf, kgf, dyn)

## Results

- Spring rate k
- Spring index C
- Total coils
- Solid height
- Deflection at the load
- Shear stress at the load

## Formula

```
k = G·d⁴ / (8·D³·N_a),  D = OD − d,  τ = K_w·8·F·D/(π·d³)
```

## Explanation

A spring's rate depends on its geometry: thicker wire makes it much stiffer (d⁴), wider coils and more coils make it softer. Car suspension, valve and mattress springs are all specified this way.

### How to use the Spring Rate Calculator

- **Wire diameter d**
- **Diameter given**
- **Diameter**
- **Active coils N_a**
- **Material**
- **End type**
- **Load (optional)**

Results update as you type, every field has its own unit menu, and everything is calculated in your browser.

### How it works

Enter the wire diameter, the outside diameter, the number of active coils and the material, plus a load to check the deflection and stress.

### Inputs explained

FieldWhat to enterWire diameter dUnits: mm, cm, m, in, µmDiameter givenChoose one: Outer diameter, Inner diameterDiameterUnits: mm, cm, m, in, µmActive coils N_aA numberMaterialChoose one: Music wire (ASTM A228), Hard-drawn steel (A227), Oil-tempered steel (A229), Chrome vanadium (A231) …End typeChoose one: Squared and ground ends, Squared (closed) ends, not ground, Plain ends, Plain and ground endsLoad (optional)Units: N, kN, MN, mN, lbf, kgf …

### What each result means

- **Spring rate k** = [Material]×[Wire diameter d]^4÷(8×[Mean coil diameter]^3×[Active coils N_a])
- **Spring index C** = [Mean coil diameter]÷[Wire diameter d]
- **Deflection at the load** = [Load (optional)]÷[Spring rate k]
- **Shear stress at the load** = ((4×[Spring index C] - 1)÷(4×[Spring index C] - 4) + 0.615÷[Spring index C])×8×[Load (optional)]×[Mean coil diameter]÷(pi×[Wire diameter d]^3)

### Example values

How the main result changes when **Wire diameter d** changes and everything else stays at the example values above:

Wire diameter d (mm)Spring rate k (N/m)1.5497.97042.252,778.612339,710.89053.7526,308.15254.560,761.78936241,204.9861

## Worked example

Inputs — Wire diameter d: 3 mm; Diameter given: Outer diameter; Diameter: 25 mm; Active coils N_a: 8; Material: Music wire (ASTM A228); End type: Squared and ground ends; Load (optional): 100 N.

Results — **Spring rate k = 9,710.89054 N/m**; Spring index C = 7.333; Total coils = 10; Solid height = 30 mm; Deflection at the load = 10.2977 mm; Shear stress at the load = 249.4631 MPa.

## Key terms

- **Spring rate**: Force per unit deflection.

## FAQ

**How does wire size affect the rate?**
Rate rises with the fourth power of the wire diameter.

**Do inactive end coils count?**
No – only active coils determine the rate.

**What is G for spring steel?**
About 79–82 GPa.

**How do springs combine?**
In series, 1/k adds; in parallel, k adds.


## Sources

- [Shigley's Mechanical Engineering Design (Budynas & Nisbett) – reference text](https://www.mheducation.com/highered/product/shigley-s-mechanical-engineering-design-budynas/M9780073398204.html)
- [The Engineering ToolBox](https://www.engineeringtoolbox.com/)