Torsion Spring Force Calculator

Calculator Inputs

Rate source

Spring rate

Spring rate unit

Rotation angle

Angle unit

Motion direction

Preload torque

Preload unit

Moment arm

Arm unit

Number of springs

Wire diameter

Mean coil diameter

Geometry unit

Active coils

Young modulus

Modulus unit

Allowable stress

Use MPa.

Formula Used

Torque from known rate: T = T_preload + kθ

Force at arm: F = T / r

Work for winding: E = T_preloadθ + 0.5kθ²

Geometry rate estimate: k = Ed⁴ / 64DN

Stress estimate: σ = K × 32T / πd³

T is torque. F is linear force. r is moment arm. k is spring rate. θ is angle in radians. E is Young modulus. d is wire diameter. D is mean coil diameter. N is active coil count.

How to Use This Calculator

Choose whether to use a known rate or a geometry estimate.
Enter the working rotation angle and its unit.
Add preload torque if the spring is already loaded.
Enter the effective arm length from the spring axis.
Add wire, coil, modulus, and stress values for checks.
Press Calculate to show results below the header.
Use CSV or PDF buttons to save the same result.

Example Data Table

Case	Rate	Angle	Preload	Arm	Springs	Approx Force
Small hinge	10 N-mm/deg	30 deg	0 N-mm	40 mm	1	7.5 N
Return lever	15 N-mm/deg	45 deg	100 N-mm	50 mm	1	15.5 N
Double lid	25 N-mm/deg	60 deg	150 N-mm	75 mm	2	44 N

Understanding Torsion Spring Force

A torsion spring stores energy when its legs rotate around the coil axis. The load is not found by weight alone. It comes from angular deflection, spring rate, preload, and arm length. This calculator brings those values together. It turns rotation into torque. Then it divides torque by the working arm to estimate linear force.

Why Accurate Inputs Matter

Small geometry changes can move the result a lot. A short arm raises force. A larger angle raises torque. Preload adds starting torque before motion begins. Two springs can share load when they are mounted evenly. Unit conversion is also important. Mixed inch, foot, millimeter, and meter inputs often cause design errors.

Engineering Checks

The tool can use a direct spring rate. It can also estimate rate from wire diameter, mean coil diameter, active coils, and modulus. The direct rate is best when a supplier gives a measured value. The geometry estimate is useful during early design. Stress is estimated from torque, wire diameter, and coil index. The safety factor compares allowable stress against calculated stress. It is a guide, not a final certification.

Practical Use

Use this calculator for hinges, levers, lids, clips, doors, traps, pedals, and return mechanisms. Start with the normal working angle. Add any preload that exists at the installed position. Enter the distance from the spring axis to the contact point. Use the same arm that actually receives the load. Review torque, force, energy, stress, and safety together.

Design Notes

A torsion spring should not be forced past its safe angular travel. Coils may close, legs may slip, or stress may exceed the chosen material limit. Always check fit, direction, cycle life, and mounting support. Prototype testing is recommended for important parts. Real springs also have tolerances. Friction and leg bending can affect measured output. Use the results as a strong starting estimate, then confirm them with supplier data and physical testing.

Also compare the opening and closing positions. Record the worst case angle. Check both clockwise and counterclockwise layouts. A correct hand direction helps the spring wind tighter under load. Wrong hand selection can reduce torque or damage legs. Keep bearings aligned, and avoid side loads where possible during repeated motion.

FAQs

1. What does torsion spring force mean?

It is the linear push or pull created when spring torque acts through a lever arm. The calculator finds torque first, then divides it by the arm length.

2. Why is the moment arm important?

Force depends directly on arm length. A shorter arm creates higher force from the same torque. A longer arm creates lower force but more travel.

3. Should I use direct rate or geometry rate?

Use direct rate when a supplier gives a tested spring rate. Use geometry rate for early estimates when wire, coil diameter, active coils, and modulus are known.

4. What is preload torque?

Preload torque is the torque already present at the installed position. It adds starting force before the spring moves through the entered working angle.

5. Can the tool calculate stress?

Yes. Enter wire diameter, mean coil diameter, and allowable stress. The calculator estimates bending stress and compares it with the allowable value.

6. What does safety factor show?

Safety factor is allowable stress divided by estimated stress. A higher value gives more margin. Final designs still need testing and supplier confirmation.

7. Are two springs handled correctly?

Yes. Enter the number of springs. The calculator multiplies total torque and force while keeping stress based on one spring.

8. What is included in CSV and PDF downloads?

Both downloads include rate, angle, preload, torque, force, energy, stress, safety factor, coil index, and allowable force guide.