Spring Constant Calculator
Stiffness Isn't Guesswork — It's a Property You Can Derive
Every spring has a stiffness that dictates how much force it takes to compress or stretch it by a given amount, and that stiffness can be found two ways: measured directly from a force and the deflection it produces, or predicted from the spring's own geometry and material before it's ever built. This calculator handles both.
The Formulas
Helical Compression Spring: k = (G × d4) / (8 × D3 × n)
In the coil formula, G is the material's shear modulus, d is wire diameter, D is coil diameter, and n is the number of active coils. Because wire diameter is raised to the fourth power, it dominates the stiffness calculation more than any other variable in the formula.
Worked Examples
| Method | Inputs | Spring Constant |
|---|---|---|
| Simple | 500 N force, 0.02 m deflection | 25,000 N/m |
| Simple | 200 N force, 0.05 m deflection | 4,000 N/m |
| Coil | G = 80 GPa, d = 3 mm, D = 25 mm, n = 10 | 5,184 N/m |
| Coil | G = 75 GPa, d = 2 mm, D = 20 mm, n = 8 | 2,343.75 N/m |
A thinner wire or a wider coil both reduce stiffness sharply — wire diameter has the fourth-power effect while coil diameter has an inverse cube effect, so small dimensional changes in either direction move the result quickly.
Where This Calculation Matters
- Suspension and mechanism design — choosing a spring that produces the right force response over its working deflection range.
- Verifying a spring from a datasheet — predicting stiffness from wire and coil geometry when a manufacturer's stated constant needs a sanity check.
- Custom spring specification — working backward from a target stiffness to the wire diameter, coil diameter, and coil count needed to achieve it.
How to Use This Calculator
- Choose the mode: Simple (Force / Deflection) or Helical Coil Spring.
- For the simple method, enter Applied Force (N) and Deflection (m).
- For the coil method, enter Shear Modulus G (GPa), Wire Diameter (mm), Coil Diameter (mm), and Number of Active Coils.
- Select Calculate to get the spring constant.
Related Calculations
To relate the resulting force to material stress rather than spring geometry, use the Stress Strain Calculator.