Torsion Spring Calculator

Torsion Spring Formula:

\[ k = \frac{E d^4}{10.8 D N} \]

Modulus of Elasticity (E):

Wire Diameter (d):

Mean Coil Diameter (D):

Number of Active Turns (N):

turns

Spring Rate (k):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is a Torsion Spring?

A torsion spring is a type of spring that exerts torque or rotational force when twisted. It stores mechanical energy when twisted and releases it when allowed to unwind. Torsion springs are commonly used in clothespins, mouse traps, and various mechanical assemblies.

2. How Does the Calculator Work?

The calculator uses the torsion spring formula:

\[ k = \frac{E d^4}{10.8 D N} \]

Where:

\( k \) — Spring rate (torque per angular displacement, N·m/deg)
\( E \) — Modulus of elasticity of the material (Pa)
\( d \) — Wire diameter (m)
\( D \) — Mean coil diameter (m)
\( N \) — Number of active turns (unitless)

Explanation: The equation relates the spring's physical dimensions and material properties to its torsional stiffness.

3. Importance of Spring Rate Calculation

Details: Calculating the spring rate is essential for designing mechanical systems that require precise torque characteristics. It helps engineers select or design springs that will provide the desired rotational force for a given angular displacement.

4. Using the Calculator

Tips: Enter all values in the specified units. Ensure wire diameter and coil diameter are in meters, and modulus of elasticity is in Pascals. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is a typical modulus of elasticity for spring steel?
A: For common spring steels, E is typically around 200 GPa (200 × 10⁹ Pa).

Q2: How does wire diameter affect spring rate?
A: Spring rate increases with the fourth power of wire diameter, making it the most influential parameter.

Q3: What's the difference between active and total turns?
A: Active turns are those that participate in deflection. Total turns include inactive ends that don't contribute to spring action.

Q4: Can this formula be used for any material?
A: Yes, as long as you use the correct modulus of elasticity for the material.

Q5: How accurate is this calculation?
A: This provides a theoretical spring rate. Actual performance may vary slightly due to manufacturing tolerances and end conditions.