Calculate spiral torsion spring torque, modulus, deflection, length, width or thickness from any five inputs with unit options and steps.
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Spiral Torsion Spring Formula
The calculator uses the flat strip spiral torsion spring relationship between torque, angular deflection, material stiffness, and strip geometry. In base units, modulus is in MPa, dimensions are in mm, angular deflection is in radians, and torque is in Nmm.
M = (E*b*t^3*theta)/(12*L) E = (12*M*L)/(b*t^3*theta) theta = (12*M*L)/(E*b*t^3) L = (E*b*t^3*theta)/(12*M) b = (12*M*L)/(E*t^3*theta) t = ((12*M*L)/(E*b*theta))^(1/3)
- M = torque or moment applied to the spiral torsion spring
- E = modulus of elasticity of the spring material
- b = strip width
- t = strip thickness
- theta = angular deflection, in radians
- L = active strip length of the spring
If torque is the missing value, the calculator applies the main formula directly. If modulus, deflection, length, width, or thickness is missing, it rearranges the same equation to solve for that value. Thickness has a cube-root relationship because strip thickness is raised to the third power in the spring stiffness term.
Common Material Modulus Values and Unit Conversions
Use a modulus value that matches your actual spring material when possible. The table below gives typical starting ranges.
| Material | Typical Modulus of Elasticity | Use Note |
|---|---|---|
| Spring steel | 200 to 210 GPa | Common for high-stiffness springs |
| Stainless spring steel | 190 to 200 GPa | Often used where corrosion resistance matters |
| Phosphor bronze | 110 to 125 GPa | Used for electrical and corrosion-resistant applications |
| Beryllium copper | 125 to 130 GPa | Good strength and conductivity |
| Brass | 95 to 110 GPa | Lower stiffness than steel |
These are the main conversions used before the formula is evaluated.
| Quantity | Conversion to Base Unit | Base Unit |
|---|---|---|
| Modulus | 1 GPa = 1000 MPa | MPa |
| Modulus | 1 psi = 0.006894757 MPa | MPa |
| Angle | 1 degree = 0.01745329252 radians | radians |
| Length, width, thickness | 1 in = 25.4 mm | mm |
| Torque | 1 Nm = 1000 Nmm | Nmm |
| Torque | 1 lbf·in = 112.984829 Nmm | Nmm |
Example Calculations
Example 1: Calculate torque
Suppose you enter a modulus of 200 GPa, angular deflection of 90 degrees, length of 500 mm, width of 10 mm, and thickness of 1 mm.
Convert the angle first: 90 degrees = 1.5708 radians. Convert the modulus: 200 GPa = 200,000 MPa.
M = (200000*10*1^3*1.5708)/(12*500) = 523.6 Nmm
The torque is approximately 523.6 Nmm.
Example 2: Calculate thickness
Suppose you enter torque of 1000 Nmm, length of 400 mm, modulus of 200 GPa, width of 20 mm, and angular deflection of 30 degrees.
Convert the angle first: 30 degrees = 0.5236 radians. Convert the modulus: 200 GPa = 200,000 MPa.
t = ((12*1000*400)/(200000*20*0.5236))^(1/3) = 1.318 mm
The required strip thickness is approximately 1.318 mm.
FAQ
What length should you enter for a spiral torsion spring?
Enter the active strip length, meaning the length of the spring material that bends and stores energy. This is not the outside coil diameter. For a flat spiral spring, it is usually the developed or unwound length of the working strip.
Should angular deflection be entered in degrees or radians?
You can enter either. The formula uses radians internally, so degree values are converted before calculation. For reference, 180 degrees equals pi radians, and 90 degrees equals about 1.5708 radians.
Why does thickness affect the result so strongly?
Thickness is cubed in the formula. Doubling the strip thickness increases the torque for the same deflection by about 8 times, assuming the same material, width, and active length. Because of this, small thickness changes can create large changes in spring torque.
