How it works
The spring rate (or spring constant) k is the force a
helical compression spring produces per unit of deflection. From the geometry and
material it is:
k = G · d⁴ / (8 · D³ · Nₐ)
where G is the shear modulus, d the wire diameter,
D the mean coil diameter and Nₐ the active coils. Because
the wire diameter enters to the fourth power, it is by far the most powerful way to
change stiffness. The rate is independent of free length and end type. For the full
story — Wahl-corrected stress, solid height and buckling — use the
compression spring calculator, and see
the spring rate formula explained.
Worked example
Music wire, d = 2 mm, mean coil D = 16 mm (spring index
C = 8), Nₐ = 6 active coils, with G = 79.3 GPa:
k = 79 300 · 2⁴ / (8 · 16³ · 6) ≈ 6.45 N/mm
So every millimetre of compression takes about 6.45 N (≈ 36.8 lbf/in). At 20 mm of deflection the force is about 129 N. Those are the numbers the calculator shows for these inputs.
Spring material data
The shear modulus G for common spring materials — the only material
property the rate depends on. The calculator fills it in when you choose a material.
| Material | Standard | Shear modulus G — GPa (Mpsi) |
|---|---|---|
| Music wire | ASTM A228 | 79.3 (11.5) |
| Oil-tempered | ASTM A229 | 77.2 (11.2) |
| Hard-drawn | ASTM A227 | 77.2 (11.2) |
| Chrome silicon | ASTM A401 | 77.2 (11.2) |
| Chrome vanadium | ASTM A232 | 77.2 (11.2) |
| Stainless 302/304 | ASTM A313 | 69 (10) |
Source: Standard spring-design references (Shigley; ASTM wire standards).
Frequently asked questions
- What is spring rate (and is it the same as spring constant)?
- Yes — spring rate and spring constant are the same thing: the force needed per unit of deflection, in N/mm or lbf/in. For a helical compression spring it is k = G·d⁴/(8·D³·Nₐ).
- How do I calculate spring rate from two measurements?
- If you have two load points, the rate is the slope: k = (F₂ − F₁) / (x₂ − x₁), the change in force divided by the change in deflection. A genuinely linear spring gives the same k anywhere on the curve; the formula above predicts that same value from the geometry.
- What are the units of spring rate?
- N/mm in SI or lbf/in in imperial — toggle in the header. They convert as 1 N/mm ≈ 5.71 lbf/in.
- How do I make a spring stiffer or softer?
- Wire diameter is the strongest lever (rate ∝ d⁴), then coil diameter (rate ∝ 1/D³) and active coils (rate ∝ 1/Nₐ). A 20% thicker wire roughly doubles the rate.
- Does free length or end type change the rate?
- No. The rate depends only on the wire, coil diameter, active coils and material. Free length and end type affect solid height and buckling, not the rate — see the full compression spring calculator for those.
Method & assumptions
- Linear (constant-rate) helical compression spring; the rate is the same at any deflection up to solid.
- Rate depends only on wire diameter, mean coil diameter, active coils and shear modulus.
- For stress, solid height and buckling, use the compression spring calculator.
Related calculators
- Compression Spring Calculator — Rate, Wahl-corrected stress, solid height and buckling, with built-in material data.
- Extension Spring Calculator — Rate, spring index and force at extension including initial tension.
- Spring Constant Calculator — Spring constant from two measured load/deflection points (Hooke’s law).