Inputs
Disclaimer
This calculator returns engineering estimates from standard, SMI-aligned spring formulas and idealized assumptions. Results are for preliminary design and RFQ preparation only, and should be verified by a qualified engineer before use in any critical application.
It does not account for every factor that affects real-world spring performance — including material lot variation, manufacturing tolerances, leg/arm geometry and mounting, operating temperature and environment, set and relaxation, or fatigue and cycle life.
Use at your own risk. Do not rely on these results where spring failure could cause injury, property damage, or loss of function. Always follow the applicable engineering standards, test for your specific application, and contact Tri-Matic Spring for a verified, production-ready specification.
Results
What the measurements mean
The three geometry fields above map straight onto this drawing. Wire Diameter (d) is the thickness of the wire itself. Outer Diameter (OD) is measured across the outside of the coil body, not across the wire. Body Coils (N) counts the full turns between the two legs.
How this torsion spring calculator works
A torsion spring stores energy in bending, not torsion, despite the name — the wire bends around the coil axis as the legs rotate toward each other. That is why this calculator uses Young’s modulus E rather than the shear modulus G used for compression and extension springs, and why the stress reported is a bending stress.
How do you calculate a torsion spring’s rate?
krev = E d⁴ / (10.8 D N) M = krev · (θ/360) krev = torque per revolution · reported per degree · θ = deflection in degrees · N = body coils
Rate is quoted per degree here, which is how torsion springs are normally specified, and torque scales linearly with angle. As with compression springs, the fourth-power relationship on wire diameter dominates everything: wire size is the coarse adjustment, coil count the fine one.
Which stress number should you design to?
σ = 32M/(πd³) σinner = Ki · σ Ki = (4C²−C−1)/(4C(C−1)), the inner-fibre curvature factor
The calculator shows both. The uncorrected figure is the one the industry usually quotes and compares against published design-stress tables. The inner-fibre figure is the true peak, on the inside surface of the coil, where a torsion spring actually cracks. On a tight-index spring the difference is significant, so design tight springs to the inner number.
Which direction should a torsion spring be loaded?
Results assume the spring is loaded in the wind-up direction, closing the coils. Loading a torsion spring the other way, unwinding it, raises stress and is not recommended — it also grows the coil diameter instead of shrinking it. The calculator reports loaded inside diameter because the body winds down as it deflects; if the spring runs over a shaft or mandrel, that shrinking bore is what determines whether it binds.
When does this estimate stop being reliable?
Body only, static, idealised. Leg geometry is not modelled, and legs contribute meaningfully to both deflection and stress in short-legged designs. Also excluded: fatigue and cycle life, friction against a mandrel or housing, set under sustained load, temperature, and production tolerance. Estimated weight is body wire alone. For anything cyclic or safety-related, send us the requirement.
What units does the calculator use?
Inches with in-lbf, in-lbf/deg and psi, or millimetres with N-mm, N-mm/deg and MPa. Deflection is in degrees in both systems.