Spring Constant Calculator Formula
Understand the math behind the spring constant calculator. Each variable explained with a worked example.
Formulas Used
Spring Constant (k)
spring_k = g_mpa * pow(wire_dia, 4) / (8 * pow(coil_dia, 3) * active_coils)Spring Index (C = D/d)
spring_index = coil_dia / wire_diaVariables
| Variable | Description | Default |
|---|---|---|
shear_mod | Shear Modulus (G)(GPa) | 79.3 |
wire_dia | Wire Diameter (d)(mm) | 3 |
coil_dia | Mean Coil Diameter (D)(mm) | 25 |
active_coils | Number of Active Coils (Na) | 10 |
g_mpa | Derived value= shear_mod * 1000 | calculated |
How It Works
Helical Spring Constant
The stiffness of a helical compression or extension spring depends on material properties, wire size, and coil geometry.
Formula
k = G d^4 / (8 D^3 Na)
where G is the shear modulus, d is wire diameter, D is mean coil diameter, and Na is the number of active coils. The spring index C = D/d should be between 4 and 12 for practical manufacturability.
Worked Example
A steel spring with 3 mm wire, 25 mm mean coil diameter, 10 active coils, G = 79.3 GPa.
shear_mod = 79.3wire_dia = 3coil_dia = 25active_coils = 10
- 01G = 79,300 MPa (= N/mm^2)
- 02d^4 = 3^4 = 81
- 03D^3 = 25^3 = 15,625
- 04k = 79,300 x 81 / (8 x 15,625 x 10)
- 05k = 6,423,300 / 1,250,000 = 5.139 N/mm
- 06Spring index C = 25/3 = 8.33 (good, within 4-12 range)
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