How to design a compression spring

Catalog problems run forward — here is a spring, what does it do. Design runs backward: the load is fixed and the spring is the unknown. Three equations carry you from the requirement to a geometry, and four checks tell you whether that geometry survives.

The three-equation chain

k = F / x · d = D / C · Na = G·d⁴ / (8·D³·k)

Rate from the requirement; wire from the envelope and a chosen spring index; coils from the rate equation solved for Na. Only two decisions are yours — the mean diameter D (set by the bore or rod it lives on) and the index C (start at 8). The spring design calculator runs the chain plus every check below from those inputs.

Worked example — 50 N at 10 mm

A spring that must push 50 N after 10 mm of travel, living on a 20 mm mean diameter, music wire, C = 8, free length 60 mm, closed & ground ends:

k = 50/10 = 5 N/mm · d = 20/8 = 2.5 mm · Na = 9.7 (11.7 total) · OD 22.5 / ID 17.5 mm

The checks come back clean: corrected shear stress 193 MPa against an 871 MPa allowable (22%), solid height 29.2 mm leaving 30.8 mm of travel to solid — the working point uses a third of it. Index 8 and 9.7 coils both sit mid-band.

The four checks that kill first passes

• Stress ratio. Wahl-corrected shear against the material allowable — past ~85% is marginal for static service, past 100% is a redesign (bigger wire, bigger D, or a stronger material).
• Travel to solid. The working deflection needs real margin before coil-bind; a spring that binds in service fails hard. More free length or fewer coils buys margin.
• Index window. C under 4 stresses and resists coiling; over 12 flops and tangles.
• Coil count. Under ~3 active coils the rate is unreliable (end effects dominate); over ~20 consider a larger wire on a larger D at the same rate.

Round, then re-check

The chain returns exact numbers; springs are wound from stock wire in standard gauges and practical fractions of a coil. Round d to a purchasable size (the wire size calculator works the gauge tables) and Na to the nearest half coil, then run the rounded geometry forward through the compression spring calculator — rate moves with d⁴, so a one-gauge rounding shifts it noticeably. Material allowables live in the spring wire properties table, the rate math in the spring rate formula guide, and cyclic duty in the fatigue life calculator.

Common mistakes

• Designing on outside diameter. The equations use mean diameter D; the spring's OD is D + d. Fitting a bore means OD plus clearance, so back the mean diameter out first.
• Specifying the load at free length. Force only exists with deflection — the requirement is a load at a height, and the travel from free length to that height sets the rate.
• Forgetting end coils. Closed ends add roughly two inactive coils: they buy squareness and seating but add solid height without adding rate.
• Shipping the unrounded design. 9.68 active coils of 2.47 mm wire is not a real spring; round, re-check, and only then quote.

Frequently asked questions

How do you design a compression spring from a load?

Three equations in a row: rate k = F/x from the load and travel; wire d = D/C from the coil diameter and a target spring index; active coils Na = G·d⁴/(8·D³·k) from the rate equation. A 50 N load at 10 mm travel on a 20 mm coil at C = 8 gives k = 5 N/mm, d = 2.5 mm and 9.7 active coils in music wire.

What spring index should I target?

C = D/d between 4 and 12, with 6–10 the usual starting band. Below 4 the coiling is hard on tooling and the Wahl stress correction grows fast; above 12 the spring is floppy, tangles in handling and holds diameter poorly. C = 8 is a safe first pass.

Why does solid height matter in spring design?

Because the working point must land well short of coil-bind. The worked design is 29.2 mm solid against a 60 mm free length — 30.8 mm of travel to solid, of which the load uses only 10 mm. A spring that can reach solid in service must carry the solid-height stress, a much harsher requirement.

Does this size a spring for fatigue?

No — the first pass checks static stress against the material allowable (the example runs at 22% of allowable, comfortable). Cyclic applications add fatigue, set removal and surge-frequency checks on top; run the candidate geometry through the fatigue life calculator before committing.