Torsion Spring Calculator

A torsion spring resists twisting, storing energy as it winds up.

How the Math Works

The torsion spring rate (k) is calculated using the formula k = E·d⁴ ÷ (64·D·n), where E is the modulus of rigidity (a material property), d is the wire diameter, D is the mean coil diameter, and n is the number of active coils. This equation shows that the spring rate is directly proportional to the fourth power of the wire diameter, meaning even small changes in thickness dramatically affect stiffness. It is also inversely proportional to both the mean coil diameter and the number of coils, so larger or more coiled springs resist twisting less. The modulus of rigidity (E) reflects how much the material deforms under stress, with stiffer materials like steel yielding higher rates for the same geometry.

Practical Applications

Engineers and designers use this calculator to select or design torsion springs for specific applications, such as automotive components, industrial mechanisms, or consumer products. By inputting material properties (E) and geometric parameters (d, D, n), they can determine the spring's resistance to angular deflection, ensuring it meets load requirements. For example, a garage door's torsion spring must lift the door's weight, so designers adjust these variables to achieve the precise torque needed. The formula also helps in reverse-engineering existing springs by measuring physical dimensions to verify if they meet design specifications.

Day-to-Day Use

This calculation ensures the reliability of everyday devices like car door latches, clothespins, and spring-loaded pens. When replacing a broken spring, knowing the correct rate prevents improper function—such as a garage door that won’t open smoothly or a door that slams shut too forcefully. Homeowners and DIY enthusiasts can use the tool to match replacement springs to existing hardware, avoiding costly mistakes. Even in hobbies like model building or robotics, understanding torsion spring rates helps create balanced, functional mechanisms with predictable performance.

Worked example

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

FAQ