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Spring Rate & Force Calculator

Design a compression spring in seconds. Enter wire diameter, coil diameter, free length, and material. See spring rate, force, stress, and solid height update live.

Inputs

Results

Spring Rate (k)
0 lb/in
Force at Target Deflection 0 lbs
Solid Height 0 in
Max Deflection to Solid 0 in
Shear Stress at Target 0 psi
Spring Index (C = D/d) 0
Safety Factor --
Formulas used:
k = Gd⁴ / (8D³N)   •   F = k × δ
τ = 8FD / (πd³) × Kw
Kw = (4C-1)/(4C-4) + 0.615/C (Wahl factor)
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Uses Lame's thick-wall cylinder equations. Verify critical designs with FEA.

How Compression Springs Work

A compression spring pushes back when squeezed. The more you squeeze it the more force it pushes back with. The relationship is linear. Double the squeeze, double the force.

Spring Rate

Spring rate k tells you how much force per inch of compression. A 20 lb/in spring needs 20 pounds to compress it one inch. And 40 pounds to compress it two inches. Spring rate is the most important number in spring design.

What Affects Spring Rate?

Four things change spring rate. Wire diameter, coil diameter, number of coils, and material. Wire diameter matters most. Doubling wire diameter increases rate by sixteen times. Adding more coils makes the spring softer. Thicker wire makes it stiffer.

Pro tip: If your spring is too stiff, add more coils. If it is too soft, use bigger wire. Changing the coil diameter is a last resort because it also changes stress.

Spring Index

Spring index C equals the mean coil diameter divided by wire diameter. Good springs have C between 4 and 12. Index of 6 to 8 is ideal. Too low and the spring is hard to make. Too high and the spring buckles when compressed.

Shear Stress

When a spring compresses, the wire twists. This creates shear stress inside the wire. The Wahl factor accounts for the stress concentration on the inside of the coil. Keep stress below the material limit for a long spring life.

Solid Height

Solid height is the length when all coils touch. You cannot compress past this point. Design your spring so the operating deflection stays safely below solid. If you need more travel, use a longer free length or more coils.

Frequently Asked Questions

Spring rate k is how much force is needed to compress the spring by one inch. Units are pounds per inch (lb/in) or newtons per millimeter (N/mm). A stiffer spring has a higher rate. It takes more force to move it the same distance.
Spring rate k = G times d to the fourth divided by 8 times D cubed times N. G is the shear modulus of the wire material. d is the wire diameter. D is the mean coil diameter. N is the number of active coils. This calculator does the math for you.
Total coils includes the end coils that rest on surfaces. Active coils are the ones that actually compress. For closed and ground ends subtract two coils. For plain ends subtract nothing. This calculator uses active coils directly.
Spring index C is the ratio D over d. A good design range is 4 to 12. Too low and the spring is hard to wind. Too high and the spring buckles. Index of 6 to 8 is ideal for most springs.
Solid height is the compressed length when all coils touch. It equals total coils times wire diameter for closed ends. You cannot compress past solid height without damaging the spring. This calculator shows the solid height so you know the minimum compressed length.
Music wire (ASTM A228) is the most common. It is strong and cheap. Use it for most general applications. Stainless 302 or 17-7 PH resists corrosion. Chrome silicon handles high stress and fatigue. Inconel works at high temperature.
When a spring compresses the wire twists. This creates shear stress. Stress should stay below the allowable shear stress of the wire. Music wire allows about 40 percent of tensile ultimate. This calculator shows stress at your target force.
Start with the target force and deflection. Pick a coil diameter (usually 5 to 8 times the wire diameter). Adjust wire diameter until the spring rate and stress are acceptable. This calculator makes it easy to iterate.
The spring becomes hard to coil in production. It also concentrates stress at the inner surface of the coil. Keep C above 4 whenever possible. Consider a larger coil diameter or smaller wire.
This calculator is for compression springs. Extension springs use similar formulas for spring rate, but they have initial tension and the stress is different. We recommend compression springs whenever possible because they are more reliable.

Spring Design Guidelines

Parameter Recommended Range Warning Range Design Tip
Spring Index (C = D/d)6 to 10Below 4 or above 12Best manufacturability at 8
Active Coils (Na)5 to 30Below 3 or above 50More coils = softer spring
Deflection at SolidBelow 80% of travelAbove 90% of travelNever design to solid height
Shear StressBelow 40% of tensileAbove 60% of tensileUse static allowable for dead loads
Wire MaterialMusic wire (A228)Brittle grades in fatigueStainless for corrosion only

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