Physics

Torsion Spring Calculator

Find the rate of a helical torsion spring.

Young's modulus (GPa)

Wire diameter

Mean coil diameter

Active coils

Calculated Output

Spring rate (N·mm/rad) 555.56

Spring rate (N·mm/°) 9.696

Formula: k = E·d⁴ ÷ (64·D·n)

Step-by-Step Breakdown

1. Values used:

2. Young's modulus = 200 GPa

3. Wire diameter = 2

4. Mean coil diameter = 15

5. Active coils = 6

7. Spring rate = 555.56N·mm/rad

8. Spring rate = 9.696N·mm/°

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The math behind it

k = E·d⁴ ÷ (64·D·n), giving torque per radian of deflection.

Steel, 2 mm wire, 15 mm coil, 6 coils → about 333 N·mm/rad.

Why use Young's modulus, not shear?

Torsion springs bend their wire, so the bending modulus E applies.