Spring Calculator — Compression, Extension & Torsion
Professional spring design tool. Calculate stiffness, load, deflection, stress, safety factor, and fatigue life. Includes reverse calculator and dual performance charts.
Spring Parameters
Results & Analysis
🔄 Fatigue Life — Modified Goodman
Reverse Spring Calculator — Design from Load Requirements
Have a load but no spring yet? Enter your target load, deflection, and space constraints — get ranked spring designs instantly. Click "Use ↗" to load any result into the calculator above.
1 What is Spring Stiffness?
Spring stiffness — also called the spring constant or spring rate — defines how resistant a spring is to deformation. Measured in N/mm or lb/in, it is the force required to deflect a spring by one unit. The spring stiffness calculator formula for a helical coil spring is:
Stiffness scales with the fourth power of wire diameter — doubling d increases k by 16×. This strong sensitivity makes tight manufacturing tolerances essential.
↑ Increases Stiffness
- Larger wire diameter (d)
- Smaller coil diameter (D)
- Fewer active coils (Na)
- Higher shear modulus (G)
↓ Decreases Stiffness
- Smaller wire diameter
- Larger coil diameter
- More active coils
- Lower shear modulus material
2 Hooke's Law Explained
Hooke's Law states that force is proportional to displacement within the elastic limit. For a spring: F = k × x. This Hooke's Law spring calculator lets you solve for any one of F, k, or x given the other two.
3 How to Design a Compression Spring
A compression spring calculator simplifies the iterative design process. The key steps: define load and deflection requirements → select material → calculate target stiffness k=F/x → choose wire and coil diameter (spring index C=D/d between 4–12) → compute active coils from the stiffness formula → verify stress with Wahl factor → check buckling (L₀/D < 4) and solid length clearance.
| Material | G (GPa) | Se/Sut | Best For |
|---|---|---|---|
| Music Wire (ASTM A228) | 81.5 | 45% | Dynamic, room temperature |
| Stainless Steel (ASTM A313) | 69.0 | 35% | Corrosive environments |
| Oil Tempered (ASTM A229) | 79.3 | 42% | General static loads |
| Chrome Vanadium (ASTM A231) | 79.3 | 50% | Fatigue, elevated temperature |
4 Spring Stress and Failure
The Wahl correction factor Kw accounts for curvature stress concentration at the inner coil surface: Kw = (4C−1)/(4C−4) + 0.615/C. Maximum shear stress: τ = Kw × 8FD / (π × d³). This is valid for circular wire cross-sections only. The maximum allowable shear stress is 45% of Sut for music wire under static loading. A safety factor ≥ 1.5 is recommended.
Buckling: Long springs buckle when L₀/D exceeds ~4 (unguided) or ~5.26 (guided on rod). The column support type (Fixed–Fixed, Hinged–Hinged, etc.) adjusts the effective slenderness limit. Guide the spring on a rod or inside a tube to prevent buckling.
5 Fatigue Life in Springs
The Modified Goodman criterion predicts infinite fatigue life when: τ_a/Se + τ_m/Sut ≤ 1, where τ_a is alternating shear stress, τ_m is mean shear stress, Se is the endurance limit (~45% Sut for music wire), and Sut is ultimate tensile strength. Enter min and max operating loads in the Fatigue section above to check your design.
Fatigue life is improved by: shot peening (2–3× life improvement), reducing stress amplitude, eliminating surface defects, upgrading to chrome-vanadium alloy, and preset (scragging) the spring before service.
6 Spring Calculator vs Manual Calculation
Manual spring calculation takes 10–30 minutes per design iteration. This spring rate calculator computes stiffness, stress (with Wahl factor), safety factor, fatigue life, and buckling check instantly — with live graph updates. The reverse calculator goes further: enter a load requirement and get ranked spring geometries in seconds, something that would take hours manually.
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