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.
Tips
- Mechanical advantage trades force for distance – the work stays the same.
- Gear and pulley ratios multiply torque and divide speed.
- Include efficiency losses for real machines.
- Use consistent units for diameters and lengths.
Common mistakes to avoid
- Inverting a gear ratio (driven ÷ driver vs driver ÷ driven).
- Ignoring friction losses.
- Mixing bore and radius in piston calculations.
Inputs explained
| Field | What to enter |
|---|---|
| Wire diameter d | Units: mm, cm, m, in, µm |
| Diameter given | Choose one: Outer diameter, Inner diameter |
| Diameter | Units: mm, cm, m, in, µm |
| Active coils N_a | A number |
| Material | Choose one: Music wire (ASTM A228), Hard-drawn steel (A227), Oil-tempered steel (A229), Chrome vanadium (A231) … |
| End type | Choose one: Squared and ground ends, Squared (closed) ends, not ground, Plain ends, Plain and ground ends |
| Load (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) |
|---|---|
| 1.5 | 497.9704 |
| 2.25 | 2,778.6123 |
| 3 | 9,710.8905 |
| 3.75 | 26,308.1525 |
| 4.5 | 60,761.7893 |
| 6 | 241,204.9861 |
Formula
k = G·d⁴ / (8·D³·N_a), D = OD − d, τ = K_w·8·F·D/(π·d³)
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.
Frequently asked questions
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.
What formula does the Spring Rate Calculator use?
k = G·d⁴ / (8·D³·N_a), D = OD − d, τ = K_w·8·F·D/(π·d³).