Free online torsion spring calculator — get the spring rate, maximum safe torque, maximum wind angle and bending stress in seconds, with a live 3D preview.
Rate, max torque & wind angleBending stress & Wahl factorEnglish (inch) & Metric (mm)Live 3D Preview
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Select Your Spring Type
⬇COMPRESSION
↕EXTENSION
↻TORSION
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ENTER YOUR DIMENSIONS
Results will be ±10% from middle value
Unit of Measurement
ENGLISH
METRIC
Attention: Results shown will be ±10% from middle value. | Free Length / Length Inside Hook is optional auto-calculated if left blank.
Wire Diameter (IN)
Exact
Range
–
MinMax
Outside Diameter (IN)
Exact
Range
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MinMax
Free Length (IN)
Exact
Range
–
MinMax
Total Coils
Exact
Range
–
MinMax
Closed EndsSquared, not ground
Closed & GroundSquared and ground flat
Double ClosedExtra tight coil each end
Open EndsPlain, uncut coil
Right Hand
RH — Clockwise
Left Hand
LH Counter-clockwise
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Key Results
Want these springs made?
Send us these values — wire diameter, coil diameter, coils and length — for a quote.
3D Spring PreviewFill in the Dimensions and press Calculate
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Free Online Tool
Torsion Spring Calculator — What It Works Out
This torsion spring calculator turns a few dimensions into a specification report: spring rate, maximum safe torque, maximum wind angle and the bending stress at that torque, with a live 3D preview. Enter the wire diameter, outside diameter and number of body coils, choose the material and press Calculate. It works in inches or millimetres.
Spring rate
Torque per revolution (N·mm/rev) from the wire diameter, mean coil diameter, body coils and the material’s modulus of elasticity.
Max torque and wind angle
The torque at which bending stress reaches the material’s allowable stress, and the wind angle that torque produces.
Bending stress and index
The Wahl bending factor, bending stress at maximum torque and warnings when the spring index is below 4 or above 12.
The formulas the calculator uses
Mean diameter D = OD − d Spring index C = D ÷ d Spring rate k = E · d⁴ ÷ (10.8 · D · Na) (N·mm per revolution; Na = body coils) Torque T = k · θ (θ in revolutions; k ÷ 360 gives N·mm per degree) Wahl factor Kb = (4C² − C − 1) ÷ (4C · (C − 1)) Max torque Tmax = σ(allow) · π · d³ ÷ (32 · Kb) Max wind angle θmax = Tmax ÷ k
d = wire diameter, OD = outside diameter, E = modulus of elasticity of the wire. A torsion spring is stressed in bending, so it uses E and the bending factor Kb rather than G and the shear factor. More in our torsion spring torque formula guide.
Worked example
Entering these values in the calculator above (metric, mild steel, right-hand wind) gives:
Input
Value
Wire diameter
2 mm
Outside diameter
20 mm
Total coils
8
Material
Mild steel IS 4454 (E = 200,000 N/mm²)
Wind direction
Right hand
Result
Value
Mean diameter / spring index
18 mm / 9
Active coils
8
Spring rate
2057.6 N·mm/rev (5.72 N·mm per degree)
Wahl bending factor
1.0903
Maximum safe torque
504.3 N·mm (5.14 kgf·cm)
Maximum wind angle
88.2° (0.245 rev)
Bending stress at maximum torque
700 N/mm²
Body length
16 mm
Check by hand: k = 200,000 × 2⁴ ÷ (10.8 × 18 × 8) = 2057.6 N·mm/rev. The torque at a 45° wind is then about 5.72 × 45 ≈ 257 N·mm.
Design notes for torsion springs
Load a torsion spring in the direction that tightens the coils. As the spring winds up its coil diameter shrinks and its body gets longer, so it needs a supporting rod (arbor) with clearance. The calculator treats every body coil as active and does not add the small deflection contributed by the legs, nor check leg stress or arbor clearance; send us your drawing for those checks. The form also shows free-length and end-configuration fields because it is shared with the other spring types; for a torsion spring they do not change the rate or torque shown.
How to use the torsion spring calculator
Choose units. Select English (inch) or Metric (mm). Torsion is already selected as the spring type.
Enter the dimensions. Enter the wire diameter, outside diameter and the number of body coils.
Select the material and wind direction. Choose the wire material (music wire, hard drawn, stainless steel, mild steel and more) and left or right hand wind.
Calculate. Enter your name and 10-digit mobile number, then press Calculate.
Review and request a quote. Check the spring rate, maximum torque and wind angle, then send the specification to us on WhatsApp for a quote.
Frequently asked questions
How do I calculate the rate of a torsion spring?
Spring rate k = E·d⁴ / (10.8·D·Na), in N·mm per revolution, where E is the modulus of elasticity, d the wire diameter, D the mean coil diameter and Na the number of body coils. Torque = k × wind angle in revolutions; divide k by 360 for the rate per degree.
Why does the formula use 10.8?
The theoretical constant is about 10.2. The practical value 10.8 is slightly higher to allow for friction between the coils and the arbor, and it is the constant the calculator uses.
What is the maximum safe torque?
It is the torque at which the bending stress in the wire reaches the allowable bending stress for the chosen material, using the Wahl bending factor Kb. The allowable values are mid-range estimates, so treat the figure as a design guide.
Why is a torsion spring stressed in bending and not shear?
When the legs rotate, the wire of the coils is bent. In compression and extension springs the wire is twisted, which is why those use shear stress and the shear modulus G instead.
Which direction should a torsion spring be loaded?
In the direction that winds the coils tighter. Loading it in the unwinding direction raises the stress, so state the direction of wind (left or right hand) when you order.
Does the calculator include the legs?
It treats every body coil as active and does not add the small extra deflection from the legs, so a real spring with long legs deflects slightly more. It also does not check leg stress or arbor clearance — send us your drawing for that.
Can you manufacture the torsion spring I design here?
Yes. Send the specification to Gurudatta Trading Co. on WhatsApp from the results page and we will quote and make it to your drawing or sample, with the leg style you need.