A spring rate calculator for compression springs
The spring rate, or spring constant, is the force needed to compress a spring by one unit of length. This spring rate calculator works it out for a round-wire compression spring from the wire diameter, the coil diameter, the number of active coils and the wire material, in millimetres and newtons or in inches and pounds-force.
It also gives the force at a chosen deflection, the shear stress in the wire with the Wahl correction, the solid height for your end type and the load and stress when the spring is fully closed. If you already know the rate you need, switch the mode and it solves for the number of active coils instead.
The results follow the standard design equations. They are a first-pass check: real springs vary with wire tolerance, setting and heat treatment, and fatigue, relaxation and buckling need separate design checks, so confirm critical springs with the manufacturer.
How to use the Spring Rate Calculator
- Choose metric or imperial units and whether to find the rate or the coils for a target rate.
- Enter the wire diameter and the coil diameter, picking whether it is the mean, outer or inner diameter.
- Enter the active coils, the end type and the free length.
- Select the wire material, or enter your own shear modulus.
- Enter a deflection to see the load and stress, and read the table for the whole working travel.
Spring Rate Calculator features
Rate and coils
Find the rate from the coils, or the coils for a target rate.
Wahl-corrected stress
Shear stress at your load and at solid height.
End types
Solid height for plain, ground, squared and squared-and-ground ends.
Metric and imperial
mm, N, MPa or in, lbf, psi with the right shear modulus.
Spring rate formulas
For a helical compression spring the rate is k = G d⁴ ÷ (8 D³ Na), where G is the shear modulus of the wire, d the wire diameter, D the mean coil diameter and Na the number of active coils. The force at a deflection x is F = k x, and the shear stress is τ = Kw × 8 F D ÷ (π d³) with the Wahl factor Kw = (4C − 1) ÷ (4C − 4) + 0.615 ÷ C and spring index C = D ÷ d.
Example: spring steel (G = 79.3 GPa) wire of 2 mm, mean diameter 16 mm and 8 active coils gives k = 79,300 × 16 ÷ (8 × 4,096 × 8) = 4.84 N/mm. With squared and ground ends there are 10 total coils and a solid height of 20 mm. A 10 mm deflection needs 48.4 N and produces about 292 MPa shear stress.
| End type | Total coils | Solid height |
|---|---|---|
| Plain | Na | d (Nt + 1) |
| Plain and ground | Na + 1 | d Nt |
| Squared (closed) | Na + 2 | d (Nt + 1) |
| Squared and ground | Na + 2 | d Nt |
Practical limits
- Keep the spring index between about 4 and 12: tighter springs are hard to make and looser ones tangle.
- Springs longer than about four times their coil diameter can buckle, so guide them on a rod or in a bore.
- The static shear stress shown must stay below the allowable value for your wire, which depends on material, diameter and whether the spring is pre-set.
- Cycling springs need a fatigue check, and hot or corrosive environments change the shear modulus.
Spring Rate Calculator FAQ
How do I calculate spring rate?
k = G d⁴ ÷ (8 D³ Na). With G = 79,300 N/mm², d = 2 mm, D = 16 mm and 8 coils the rate is 4.84 N/mm.
What are active coils?
The coils that deflect under load. Squared or ground end coils touch the seat and do not count, so total coils exceed active coils by 1 or 2 for most end types.
How do I find the force at a deflection?
Multiply the rate by the deflection. A 4.84 N/mm spring compressed 10 mm carries 48.4 N.
What shear modulus should I use?
About 79 GPa (11.5 Mpsi) for spring steel, 69 GPa for stainless 302/304, 41 GPa for phosphor bronze. These are typical values; use your supplier’s figure for important work.
Does this work for extension or torsion springs?
No. It is for round-wire helical compression springs; extension springs share the rate formula but have initial tension and hooks, and torsion springs use a different formula.
Can I enter the outer diameter?
Yes. Choose "outer" next to the coil diameter and the calculator subtracts the wire diameter to get the mean diameter.