Torsion Spring Torque & Rate Formula (with worked example)
Quick answer: Torsion spring rate is k = E·d⁴ / (64·D·N) in N·mm per radian, where E is the modulus of elasticity, d wire diameter, D mean coil diameter and N active coils; torque = k × angle.
By Gurudatta Trading Co., Mumbai · Updated 2026-09-28
The formula
k = E · d⁴ / (64 · D · N) (N·mm per radian) and T = k · θ
- E — modulus of elasticity (steel is about 207,000 MPa)
- d — wire diameter, D — mean coil diameter, N — active coils
- θ — deflection angle in radians (degrees × π / 180)
Worked example
d = 2 mm, D = 18 mm, N = 8, E = 207000 MPa: k ≈ 359.38 N·mm/rad (about 6.27 N·mm per degree). A 90° deflection gives a torque of ≈ 564.50 N·mm.
Practical designs often use a correction factor because of friction and leg effects, and a torsion spring should be loaded in the direction that tightens the coils. Use the calculator to check stress, and compare with the compression spring formula.
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Gurudatta Trading Co. (Mumbai, since 2000, ISO 9001:2015) manufactures compression, extension and torsion springs to drawing or sample. Use the free Spring Rate Calculator or message us on WhatsApp.
FAQs
What is the formula for torsion spring rate?
k = E·d⁴ / (64·D·N) in N·mm per radian, using the modulus of elasticity E, wire diameter d, mean diameter D and active coils N.
How do I convert torsion spring rate from radians to degrees?
Multiply the per-radian value by π/180 to get the rate per degree.
Which way should a torsion spring be loaded?
In the direction that winds the coils tighter, so the wire is in bending as designed.