Torsion Spring Calculator

A torsion spring is a type of spring that works by twisting along its axis, storing rotational energy when a torque is applied. Unlike compression or extension springs that push or pull linearly, torsion springs exert a rotational (angular) force. They are commonly found in clothespins, mousetraps, garage doors, and hinges.

The spring rate (k) of a torsion spring is the torque required to deflect the spring by one degree. It is calculated using the formula k = (E × d⁴) / (10.8 × D × Na), where E is the modulus of elasticity of the material, d is the wire diameter, D is the mean coil diameter, and Na is the number of active coils. A higher spring rate means the spring is stiffer.

The spring index (C) is the ratio of the mean coil diameter (D) to the wire diameter (d): C = D/d. It indicates the curvature of the coils. A spring index between 4 and 12 is generally recommended for manufacturability and performance. Very low indices (under 4) can cause manufacturing difficulties and high stress concentrations, while very high indices (above 12) may result in tangling or instability.

The Wahl correction factor (Kw) accounts for the additional stress at the inner surface of the coil due to curvature and direct shear effects. It corrects the theoretical stress calculation to match real-world conditions. The formula is Kw = (4C - 1)/(4C - 4) + 0.615/C. Applying this factor gives a more accurate and conservative stress estimate for spring design.

Material selection depends on load requirements, environment, and cost. Music wire (ASTM A228) offers the highest tensile strength for general-purpose applications. Stainless steel 302 is ideal for corrosive environments. Chrome silicon and chrome vanadium alloys provide excellent fatigue resistance for dynamic or high-stress applications. Phosphor bronze is used when non-magnetic or corrosion-resistant properties are needed.

The deflection angle (θ) is the angular displacement applied to the spring during operation. It directly determines the working torque: Torque = Spring Rate × Deflection Angle. Larger deflection angles produce higher torques and higher stresses in the spring wire. It is important to ensure that the stress at maximum deflection remains within the material's yield strength limits.

The outer diameter (OD) is the largest diameter of the coil as measured from outside edge to outside edge. The inner diameter (ID) equals OD minus twice the wire diameter. The mean diameter (D) is the average of OD and ID, calculated as D = OD - d. The mean diameter is the value used in most spring rate and stress calculations.

The number of active coils (Na) inversely affects spring rate — more coils produce a softer (lower rate) spring, while fewer coils produce a stiffer spring. Na also influences body length and the amount of stored energy. Torsion spring legs can add to the effective active coil count depending on their geometry, which is why leg length can affect the calculated rate.