Torsion Spring Calculator

A helical torsion spring stores energy when its ends rotate relative to one another. Although the wire is coiled, it is primarily loaded in bending rather than pure material torsion. The spring responds with a moment that opposes angular deflection. For operation within the elastic range, that response is commonly approximated as linear: M = kθ, where M is torque, k is angular spring rate, and θ is deflection from the unloaded or installed reference position. This calculator accepts spring rate in newton millimetres per degree and angle in degrees. Multiplying them gives torque in newton millimetres. Stored elastic energy is the area under the linear torque-angle curve, one half of final torque times angular displacement. For energy in joules, the calculator converts newton millimetres to newton metres and degrees to radians before applying U = Mθ/2. That unit conversion is essential; directly multiplying degree-based values does not produce joules. A catalogue spring rate is typically based on wire diameter, mean coil diameter, active coil count, elastic modulus, and a correction factor. Manufacturing tolerances, winding direction, leg geometry, body clearance, and friction around a mandrel can alter measured behavior. The rate also assumes a working range where the material remains elastic and coils or legs do not interfere. Use supplier test data when available, especially for repeated cycling or safety-critical assemblies. Angular deflection should be measured from the state associated with the stated torque. A spring may be installed with preload, so zero mechanism angle is not necessarily zero spring torque. If preload torque is known, total torque is the preload plus k times additional deflection. This simple calculator reports the incremental linear torque from the entered deflection; account for preload separately when selecting a spring or balancing a mechanism. Torsion springs appear in hinges, clips, latches, counterbalances, vehicle components, and return mechanisms. Positive and negative angle conventions depend on winding direction and viewpoint. The displayed magnitude follows the entered angle's sign, while energy is most meaningful for a loading displacement in the spring's intended direction. Confirm maximum recommended deflection, stress, and cycle-life limits with design standards or the manufacturer. The result is useful for comparing rates, checking test data, and estimating mechanism torque and energy, but it does not replace stress, fatigue, or stability analysis.