Torsion Spring Calculations

Definition of Torsion Spring Calculations:

The process of calculating several torsion spring dimensions such as the computing of shear modulus of a spring wire, youngs modulus of spring wire, poission's ratio for spring wire along with a springs wire diameter, outer diameter and number of active coils to obtain a torsion spring calculation.

Here is an easier and faster way to calculate your torsion spring calculations by using our free online spring calculator; which provides you with a full spring analysis of your spring. Just enter a few of your torsion spring's dimensions, and you'll have all the information you need to make sure your spring will function correctly in your application.

Basic Torsion Spring Calculation Formulas:

Sometimes, you might only have a couple of your torsion spring's dimensions but in order to calculate other things such as rate and travel, you'll need to know a bit more. Here you will see a couple examples of different scenarios where a certain spring dimension is needed.

To Calculate Wire Diameter:

If you only have your Outer Diameter (OD) and Inner Diameter (ID) but need Wire Diameter (WD), you must subtract your Inner Diameter (ID) from your Outer DIameter (OD) and then divide the result by two as shown in the formula below:

(Outer Diameter – Inner Diameter) ÷ 2 = Wire DIameter
(OD - ID) ÷ 2 = WD


To Calculate Outer Diameter from Inner Diameter:

Multiply your Wire Diameter by two and then add it to your Inner Diameter; as shown in the formula below.

2 * Wire Diameter + Inner Diameter = Outer Diameter
2WD + ID = OD


To Calculate Inner Diameter from Outer Diameter:

Multiply your wire diameter by two and then subtract the result from your Outer Diameter; as shown in the following formula.

Outer Diameter – 2 * Wire Diameter = Inner Diameter
OD – 2WD = ID


To Calculate Mean Diameter:

The mean diameter is calculated by taking one wire diameter and subtracting it from your torsion spring's outer diameter or adding it to the inner diameter as shown below.

Outer Diameter – Wire Diameter = Mean Diameter
OD – WD = MD Inner Diameter + Wire Diameter = Mean Diameter
ID + WD = MD


To Calculate Your Spring's Index:

This spring calculation is needed to make sure that the torsion spring you require is manufacturable. To calculate index, you must divide your mean diameter by your wire diameter as displayed in the following spring index formula.

Mean Diameter ÷ Wire DIameter = Index
MD ÷ WD = I


Advanced Torsion Spring Calculations

You'll need a spring rate that will work with the loads you plan to apply to your torsion spring as well as the degrees you plan to travel. Below you will find the torsion spring calculation for rate as well as load.

Formula to Calculate Torsion Spring Rate:

Rate Per 360 Degrees
(R) = Ed^4 / 10.8 DN

    Explanation of Symbols:
  • d = wire size (inches)
  • D = Mean Diameter (inches)
  • N = Number of active coils
  • R = Rate per 360 degrees
  • S = Stress (lbs / square in)
  • P = Load (lbs)
  • M = Moment (inch-lbs)
  • D / d = Index correction
  • E = Modulus of Elasticity
    Modulus of Elasticity "E" for common spring wires.
  • PSI x 10^6
  • Music Wire = 30 psi
  • Stainless Steel = 28 psi
  • Chrome Vanadium = 30 psi
  • Chrome Silicon = 30 psi
  • Phosphor Bronze = 15 psi

Formula To Calculate Torsion Spring Load / Force:

Multiply your spring's rate per degree by the distance traveled in degrees as shown in the following formula.

Load = Rate Per Degree * Distanced Traveled
L = RpD * DT

How to Calculate Your Torsion Spring's Rate From Load and Travel:

Divide the load by the degrees of travel to calculate the rate of your torsion spring as displayed on the formula below.

Load ÷ Distance Traveled (in degrees) = Rate
L ÷ DT = R