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Torsional Spring Torque and Energy Calculator — result sheet
Calculate elastic torque, total torque with an entered preload, angular deflection, and stored spring energy for an ideal torsional spring.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: θ = degrees × π/180; elastic spring torque = kθ; total modeled torque = preload + kθ; elastic energy = ½kθ².
A torsional spring stores energy as it rotates away from its reference position. The preload is shown separately in the total torque, while stored elastic energy uses the entered deflection from the spring’s zero reference.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Torsional spring rate — N·m/rad; minimum 1.0E-6; maximum 1000000000
- Angular deflection — degrees; minimum -360000; maximum 360000
- Entered preload torque — N·m; minimum -1000000000; maximum 1000000000
Worked example
| Input | Value |
|---|---|
| Torsional spring rate | 2 |
| Angular deflection | 45 |
| Entered preload torque | 1 |
At 45°, elastic torque is about 1.5708 N·m, total modeled torque is about 2.5708 N·m, and stored elastic energy is about 0.61685 J.
Assumptions and limits
- The spring rate is constant over the entered angular range.
- The angle is measured from the spring’s unloaded reference position and converted from degrees to radians.
- Preload is an externally entered signed torque and is not folded into elastic energy.
- The spring is ideal, elastic, and quasi-static for this calculation.
- Coil geometry, wire stress, friction, hysteresis, fatigue, end hooks, travel stops, and temperature are not modeled.
- Negative angle means the opposite rotation direction and is not automatically invalid.
- Use manufacturer data and a mechanical design review for a real spring, latch, actuator, or return mechanism.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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