Compression Spring Calculator
Spring rate, shear stress and solid height from wire size and coil geometry.
Static rate for a helical compression spring. It does not check buckling of a long spring, fatigue life under cycling, or set and relaxation — all of which matter in a spring that works for a living.
How it works
A compression spring is a torsion bar wound into a helix. The wire is not bending — it is twisting — which is why the governing property is the shear modulus G rather than Young's modulus, and why the rate depends on the fourth power of the wire diameter:
k = G d⁴ ÷ (8 D³ Nₐ)
Those exponents dominate everything. A 10% thicker wire is 46% stiffer. A 10% larger coil diameter is 25% softer. Adding one active coil to a ten-coil spring softens it by 10%. If a spring is nearly right, change the coil count; if it is badly wrong, change the wire.
Spring index — mean diameter over wire diameter — is the manufacturability number. Below 4 the wire is being bent round a radius tight enough to damage it and the coiler struggles; above 12 the spring is floppy, tangles with its neighbours in a bin and buckles in service. Between 6 and 9 is where springs are easy to make and behave.
The Wahl factor corrects for the fact that shear stress is not uniform round the wire: curvature crowds it toward the inside of the coil, so a tight spring is more highly stressed than the plain torsion formula suggests. At index 4 the correction is about 40%, at index 12 about 12% — another reason very tight springs break.
Solid height sets the hard limit on travel, and it is a real limit: coil-bound springs stop being springs and start being solid columns of steel.
Common questions
How many coils are active?
Total coils minus the dead ones at the ends. Closed ends — ground or not — cost you two, because the last coil at each end touches its neighbour and cannot deflect. Open ends have no dead coils but sit badly and buckle.
What stress can the wire take?
Music wire is usually worked to about 45% of its tensile strength for static loads and much less for fatigue — and its tensile strength rises as the wire gets thinner, from roughly 1600 MPa at 5 mm to over 2300 MPa at 0.5 mm. Under 700 MPa corrected is comfortable for most sizes; over 1000 wants checking against the actual wire spec.
Can I just cut a spring shorter?
You can, and it gets stiffer in proportion to the coils removed — halving the active coils doubles the rate. The cut end is not closed or square, so it sits crookedly and loads the spring off-axis, which is why cut springs buckle and fail early.
Will it buckle?
Likely if the free length exceeds about four times the mean diameter and both ends are free to pivot. Guide it over a rod or inside a bore if it is that slender.