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.
- 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)
Frequently Asked Questions
What affects spring stiffness the most?
Wire diameter has the strongest effect because it appears as d^4. Doubling wire diameter increases stiffness 16 times. Coil diameter is next important (D^3 in denominator).
What is the shear modulus for spring steel?
For music wire and chrome silicon steel springs, G is approximately 79.3 GPa (11.5 Mpsi). For stainless steel springs, G is about 69 GPa.
How do I count active coils?
Active coils = total coils minus inactive end coils. For closed and ground ends, subtract 2. For closed ends only, subtract 2. For plain ends, active coils equal total coils.
Learn More
Guide
Understanding Vibration Analysis: Natural Frequency, Damping, and Resonance
Learn the fundamentals of mechanical vibration analysis. Covers natural frequency, damping ratio, resonance, forced vibration, vibration isolation, and practical measurement techniques.
Ready to run the numbers?
Open Spring Constant Calculator