How this calculator works
Stiffness rises with the fourth power of wire diameter and falls with the cube of mean coil diameter. Convert outside diameter by subtracting one wire diameter, or inside diameter by adding one. Active coils exclude end coils that do not deflect appreciably. The selected end convention subtracts zero, two or four coils from the total; actual end participation depends on manufacture and seating, so use measured active count when available. The model omits direct-shear corrections and nonlinear coil contact.
Formula
k = G d⁴/(8 D³ Na); D=OD-d=ID+d; Nt=Na+inactive coils.
Worked example
For 80 GPa shear modulus, 1 mm wire, 11 mm outside diameter and 10 active coils, mean diameter is 10 mm, inside diameter is 9 mm and rate is 1000 N/m. The same dimensions at 2000 N/m require 5 active coils.
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Frequently asked questions
Can active coil count be fractional?
Yes. Partial turns and end participation can produce an effective non-integer count.
Why is outside diameter not used directly?
The wire centreline sets the torque arm and spring compliance, so the formula uses mean diameter.
Is spring rate the same as maximum load?
No. Maximum load also depends on available travel, stress limits and coil contact.