Spring Calculator | Spring Rate, Force, Deflection

📖 How to Use This Spring Calculator

Enter wire diameter (d) – The diameter of the spring wire in millimeters.

Enter mean coil diameter (D) – The average diameter of the spring coil (outer dia - wire dia).

Enter number of active coils (Nₐ) – The number of coils that actually deflect. Total coils minus end coils.

Select material modulus – Choose from common spring materials or enter a custom value.

Use presets or custom – Click presets for typical configurations or enter your own values.

🔩 What is Spring Rate (k)?

The spring rate (or spring constant) is the amount of force required to deflect the spring by one unit of length (N/mm). It's a fundamental property that determines the spring's stiffness.

The standard formula for a compression spring is:

k = (G × d⁴) / (8 × D³ × Nₐ)
where G = modulus of rigidity (GPa), d = wire diameter (mm), D = mean coil diameter (mm), Nₐ = number of active coils.

💡 Practical Applications

Automotive suspension – Coil springs, valve springs.
Industrial machinery – Press tools, actuators, dampers.
Consumer products – Ballpoint pens, mattresses, toys.
Aerospace – Landing gear, control systems.
Medical devices – Surgical instruments, implantable devices.

❓ Frequently Asked Questions (FAQ)

What is the difference between active and total coils?

Active coils are those that actually compress when the spring is loaded. Total coils include the active coils plus closed ends (usually 2-3 inactive coils).

What is the spring index (C)?

The spring index is the ratio of mean coil diameter to wire diameter (C = D/d). A good design typically has C between 4 and 16. C < 4 leads to stress concentration, C > 16 causes buckling.

What is the Wahl factor?

The Wahl factor accounts for stress concentration due to curvature and direct shear. It's used to correct the stress calculation: K = (4C - 1)/(4C - 4) + 0.615/C.

What materials can I use for springs?

Common materials include music wire (high carbon steel), stainless steel, phosphor bronze, beryllium copper, and various alloys. The modulus (G) varies by material.

How do I calculate spring force?

Force = k × deflection (F = k × x). If you know the desired deflection, multiply by the spring rate to get the required force.

What's a good spring rate for my application?

It depends on the application. For suspension: 20-100 N/mm. For valve springs: 10-50 N/mm. For small mechanisms: 0.1-10 N/mm. Always consider the required force and deflection.