Spring Rate Calculator
Calculate spring rate (spring constant) from design parameters or force measurements
Spring Rate Calculator
Steel: 80 GPa, Stainless: 77 GPa, Brass: 40 GPa
Leave empty to auto-calculate: 0.0 coils
Spring Rate Results
Formula: k = (G × d⁴) / (8 × D³ × n)
Example Calculation
Compression Spring Example
Material: Steel (G = 80 GPa)
Wire diameter (d): 2.0 mm
Outer diameter (OD): 20.0 mm
Mean diameter (D): 18.0 mm
Total coils: 10
End type: Closed & squared (2 inactive coils)
Active coils (n): 8
Calculation
k = (G × d⁴) / (8 × D³ × n)
k = (80×10⁹ × (0.002)⁴) / (8 × (0.018)³ × 8)
k = (80×10⁹ × 1.6×10⁻¹¹) / (8 × 5.832×10⁻⁶ × 8)
k = 3,424 N/m or 19.6 lbf/in
Spring Rate Basics
Definition
Force per unit length needed to compress or extend a spring
Units
N/m (SI) or lbf/in (Imperial)
Also Known As
Spring constant, spring stiffness
Spring End Types
Open Ends
All coils are active
Active coils = Total coils
Closed & Squared
2 coils are inactive
Active coils = Total - 2
Double Closed
4 coils are inactive
Active coils = Total - 4
Common Materials
Design Tips
Spring index (C = D/d) should be 4-12 for good manufacturability
Higher spring rate means stiffer spring
Smaller wire diameter decreases spring rate
More active coils decrease spring rate
Understanding Spring Rate
What is Spring Rate?
Spring rate, also known as spring constant or spring stiffness, is a measure of the force required to compress or extend a spring by a unit distance. It's expressed in N/m (newtons per meter) or lbf/in (pounds-force per inch).
Basic Formula
k = F / δ
- k: Spring rate (N/m)
- F: Applied force (N)
- δ: Displacement (m)
Design Formula
k = (G × d⁴) / (8 × D³ × n)
- G: Shear modulus (Pa)
- d: Wire diameter (m)
- D: Mean coil diameter (m)
- n: Number of active coils
Factors Affecting Spring Rate
- •Wire Diameter: Rate increases with the 4th power of diameter
- •Coil Diameter: Rate decreases with the 3rd power of diameter
- •Active Coils: Rate decreases linearly with number of coils
- •Material: Rate increases with shear modulus
Spring Index Guidelines
Note: The spring index C = D/d is crucial for manufacturing feasibility and spring performance.
Practical Applications
Automotive
- • Suspension springs
- • Valve springs
- • Clutch springs
- • Seat springs
Industrial
- • Machine tool springs
- • Die springs
- • Safety valve springs
- • Electrical contact springs
Consumer
- • Mattress springs
- • Pen springs
- • Toy springs
- • Appliance springs