Spring Rate Calculator
Calculate the spring rate of a helical compression or extension spring from wire diameter, mean coil diameter, active coils and material — with spring index, Wahl correction factor, deflection under load and corrected shear stress, in both metric and imperial units.
Input
Applies to every dimension and load below. Results are always reported in both systems.
Sets the shear modulus G. Pick Custom to enter your own value.
Diameter of the wire itself — mm in metric, inches in imperial.
Outer diameter minus one wire diameter — measured coil centre to coil centre.
Coils that actually deflect — total coils minus the closed/ground end coils (usually 2).
N in metric, lbf in imperial. Adds deflection and corrected shear stress to the results.
Output
| Metric | Value |
|---|---|
| No data yet | |
Guides
Work out the spring rate (spring constant) of a helical compression or extension spring from four numbers: wire diameter, mean coil diameter, active coil count, and the material's shear modulus. The calculator also reports the spring index, the Wahl correction factor, deflection under a load you specify, and the corrected torsional shear stress — the numbers you actually need before committing a spring to a design.
How to use it
- Pick your unit system — metric (mm, N) or imperial (inch, lbf). Every dimension and load below follows that choice.
- Choose the wire material. That fills in the shear modulus G for you; pick Custom if you're working from a mill certificate or a material the list doesn't cover.
- Enter the wire diameter (d), the mean coil diameter (D), and the number of active coils (n).
- Optionally enter an applied load to get the deflection and corrected shear stress at that load.
Results appear as you type and are reported in both metric and imperial, so you can hand the same figure to a supplier on either side of the Atlantic.
The formula
Spring rate for a round-wire helical spring is:
k = (G · d⁴) / (8 · D³ · n)
Wire diameter is raised to the fourth power and coil diameter to the third, which is why small measurement errors matter so much: getting d wrong by 5% moves the rate by more than 20%. The same formula covers compression and extension springs — an extension spring's initial tension shifts the force curve up but doesn't change its slope.
Which diameter do I measure?
Mean coil diameter — coil centre to coil centre. If you measured the outside diameter with calipers, subtract one wire diameter (D = OD − d). If you measured the inside diameter, add one (D = ID + d). Feeding an outside diameter straight in is the most common reason a calculated rate comes out too soft.
What counts as an "active" coil?
Only the coils free to deflect. On a compression spring with closed and ground ends, subtract 2 from the total coil count; with closed-but-unground ends, subtract about 1.5–2. The end coils carry load but don't flex, so counting them inflates the coil count and under-predicts the rate.
Why does spring index matter?
Spring index C = D/d describes how tightly the wire is wound. Below about 4 the wire is hard to coil and stress concentrates sharply on the inner fibre; above about 12 the coils are slack and tend to tangle and buckle. The calculator flags where your design lands. The Wahl correction factor derived from C accounts for that inner-fibre stress concentration — the corrected shear stress figure already includes it.
Limits
This is a linear-rate calculation for round wire. It doesn't check solid height, buckling, fatigue life, or set/relaxation, and it assumes a constant coil diameter (not a conical or variable-pitch spring). Verify those separately before manufacturing.
Privacy
Everything runs in your browser — no dimensions or design data are sent anywhere.
Related tools
For fastener preload on the assembly the spring sits in, use the Bolt Torque Calculator. If you're sizing a drive rather than a spring, the Belt Length Calculator covers pulley centre distances, and the Thermal Expansion Calculator handles how much the assembly grows when it heats up.