Compression Spring Calculator

Design and analyze compression springs. Calculate spring rate, deflection, stress, solid height, and more for your engineering projects.

mm
Diameter of the spring wire
mm
Average diameter of the spring coil
Number of coils that participate in deflection
Total number of coils including end coils
mm
Length of spring when no load is applied
Material affects shear modulus and allowable stress
Load & Deflection Conditions
N
mm
mm

Compression Spring Fundamentals

A compression spring is an open-coil helical spring that offers resistance to a compressive force applied axially. Compression springs are usually coiled at constant diameter, though they can be coiled in other forms.

Key Formulas:

1. Spring Rate (k): k = (G × d⁴) / (8 × D³ × N)

2. Shear Stress (τ): τ = (8 × F × D × K) / (π × d³)

3. Wahl Correction Factor (K): K = (4C - 1)/(4C - 4) + 0.615/C where C = D/d

4. Solid Height (Ls): Ls = (Nt + 1) × d (for closed and ground ends)

Where: G = Shear modulus, d = Wire diameter, D = Mean diameter, N = Active coils, F = Applied load

Spring Design Guidelines

Spring Index (C = D/d)
4 to 12
Recommended Range
Maximum Deflection
≤ 80% of available
Design Rule
Allowable Stress
45-50% of tensile strength
For static loads (with safety factor)

Design Considerations

  • Spring Index: Values between 4 and 12 are recommended. Lower values (4-7) are more difficult to manufacture but have higher stress. Higher values (8-12) are easier to manufacture but may buckle.
  • Buckling: For slender springs (free length > 4 × mean diameter), buckling may occur. Use guides or consider a higher spring index.
  • End Types: Closed ends are most common. Closed and ground ends provide better alignment and flatter bearing surfaces.
  • Set Removal: Springs are often presetted to remove permanent set and increase load-bearing capacity.
  • Fatigue Life: For dynamic applications, keep maximum stress below 35-40% of tensile strength and consider shot peening for improved fatigue resistance.

Common Applications

Automotive
Suspension, valves
Industrial
Valves, clutches
Consumer
Pens, toys, appliances

Frequently Asked Questions

Active coils are those that deflect under load and contribute to the spring's flexibility. Total coils include all coils in the spring, including the end coils that may be inactive (closed or ground ends don't deflect as much). For closed and ground ends, typically 1.5-2 coils are inactive.

Material selection depends on: 1) Required strength and stiffness, 2) Operating environment (temperature, corrosion), 3) Fatigue life requirements, 4) Cost considerations. Music wire is most common for general applications. Stainless steel is preferred for corrosive environments. Chrome alloys offer better fatigue resistance for dynamic applications.

The Wahl correction factor (K) accounts for the curvature of the wire in a helical spring. Simple torsion formulas assume a straight wire, but the curvature in springs creates additional shear stress on the inner surface of the coil. The Wahl factor increases the calculated stress, with greater effect for lower spring indices (thicker wire relative to diameter).

Typically, compression springs should not be compressed to solid height in normal operation. A safe working deflection is usually 75-80% of available deflection (free length minus solid height). For dynamic applications, even less deflection may be recommended to ensure adequate fatigue life. Always leave some clearance to prevent over-stressing.

Safety factors depend on the application: 1) Static loads with known magnitude: 1.2-1.5, 2) Static loads with variable magnitude: 1.5-2.0, 3) Dynamic/fatigue loads: 2.0-3.0 or higher. Critical applications (aerospace, medical) may require even higher factors. Always consider consequences of failure when determining safety factors.