Torsional Spring Calculator

Calculate the torque, spring rate, and potential energy stored in a torsional spring based on wire diameter, coil diameter, number of active coils, and deflection angle.

SPRING TORQUE
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Spring Rate
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Stored Energy
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Spring Index
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Max Bending Stress
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What Is a Torsional Spring?

A torsional spring is a mechanical device that stores energy when it is twisted. Unlike compression or extension springs that resist linear forces, torsional springs resist rotational forces (torque). They are used in clothespins, clipboard mechanisms, garage doors, mouse traps, and automotive suspension systems.

The spring exerts a restoring torque proportional to the angular displacement from its equilibrium position, following Hooke's law in the rotational domain. The proportionality constant is the torsional spring rate, measured in units of torque per radian (or degree) of rotation.

Torsional Spring Rate Formula

k = (E × d⁴) / (64 × D × Na)
Torque = k × θ
Energy = ½ × k × θ²

Where E is Young's modulus, d is wire diameter, D is mean coil diameter, Na is the number of active coils, and θ is the angular deflection in radians. The bending stress in the wire can be computed as σ = (32 × Torque) / (π × d³).

Spring Wire Materials

MaterialE (GPa)Typical Use
Music Wire (ASTM A228)207High-stress springs
Stainless Steel 302193Corrosion-resistant springs
Phosphor Bronze103Electrical contacts
Beryllium Copper128Low-fatigue springs

Frequently Asked Questions

What is the spring index and why does it matter?

The spring index C = D/d is the ratio of mean coil diameter to wire diameter. An index between 4 and 12 is considered practical. Too low (tight coils) causes manufacturing difficulty, and too high (loose coils) makes the spring prone to tangling.

How do I increase the torque of a torsional spring?

You can increase torque by using thicker wire (increases as d^4), reducing the coil diameter, reducing the number of active coils, or choosing a material with a higher Young's modulus. Increasing the deflection angle also increases torque proportionally.

What is the difference between torsion spring rate in N-mm/deg and N-mm/rad?

They differ by a factor of 180/pi (approximately 57.3). To convert from N-mm/rad to N-mm/deg, divide by 57.296. Always check which unit convention is being used in your design specifications.