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Calcimator

Spring Design Calculator

Design helical compression springs. Calculate spring rate, deflection, shear stress with Wahl correction, and free/solid lengths.

About this calculator

This calculator sizes a helical compression spring — the kind found in valves, latches, and machine mechanisms — from four physical inputs: wire diameter (d), mean coil diameter (D), number of active coils (N), and the wire's shear modulus (G). The core relationship is the spring rate, k = Gd⁴/(8D³N), which falls directly out of treating each coil as a torsion bar wound into a helix; because d is raised to the fourth power, small changes in wire gauge swing the stiffness dramatically. Once you apply a force, deflection is just F/k (Hooke's law), and the resulting stress in the wire is corrected with the Wahl factor, Kw = (4C−1)/(4C−4) + 0.615/C, where C = D/d is the spring index. The Wahl factor accounts for both direct shear across the wire cross-section and the curvature effect that concentrates stress on the inside of each coil — a correction that becomes more important as the spring index drops below about 6.

The calculator also reports solid length (all coils stacked flat, assuming ground-and-closed ends that add two inactive coils) and an estimated free length that adds the working deflection plus a 15% clash allowance so coils don't bottom out under load. Keep the spring index between 4 and 12: below 4 the wire is hard to coil and stress concentrations get severe; above 12 the spring is prone to buckling and tangling. This is an analytical estimate for steel-type springs — it doesn't account for surface finish, shot peening, or fatigue life, which matter for cyclic applications.

Inputs

in
in
psi
lb

Results

Spring Rate (k)

17.97 lb/in

Deflection

0.56 in

Shear Stress (Wahl)29,153 psi
Solid Length1 in
Estimated Free Length1.64 in
Spring Index (C)10
How to Use This Calculator
  1. Enter the Wire Diameter (d) in inches — common music wire spring sizes range from 0.020" to 0.500".
  2. Enter the Mean Coil Diameter (D) in inches — the average diameter of the spring coils. The spring index C = D/d should be 4–12 for practical springs.
  3. Enter the number of Active Coils (N) that deflect under load. Closed-ground end springs add 2 inactive coils.
  4. Enter the Shear Modulus (G) for the wire material: music wire ≈ 11.5 Mpsi, stainless steel ≈ 10.0 Mpsi.
  5. Enter the Applied Force in lb to calculate deflection and stress at a specific operating load.
  6. Review Spring Rate (lb/in), Deflection (in), Shear Stress (psi with Wahl correction), and estimated Free Length to verify the design fits the installation envelope.

How the result changes with Wire Diameter (d)

Wire Diameter (d)Spring Rate (k)Deflection
0.051.12 lb/in8.9 in
0.085.69 lb/in1.76 in
0.1590.97 lb/in0.11 in
0.25701.9 lb/in0.01 in

What each input means

Wire Diameter (d)
Diameter of the spring wire. Common music wire sizes range from 0.020" to 0.500".
Mean Coil Diameter (D)
Average diameter of the coil (OD - wire diameter). Spring index C = D/d should be 4-12 for practical springs.
Active Coils (N)
Number of active coils that contribute to deflection. Total coils = active + 2 for closed-ground ends.
Shear Modulus (G)
Shear modulus of the wire material. Music wire ≈ 11.5 Mpsi; stainless steel ≈ 10.0 Mpsi; phosphor bronze ≈ 6.0 Mpsi.
Applied Force (F)
Force applied to the spring for stress and deflection calculations.

How this is calculated

Worked example, using the default values

  1. Identify Input Parameters
    4 parameters
    Wire Diameter (d) = 0.1, Mean Coil Diameter (D) = 1, Active Coils (N) = 8, Shear Modulus (G) = 11500000 = 5 input(s) provided
  2. Calculate Spring Rate
    Spring Rate
    17.969 = 17.969
  3. Calculate Deflection
    Deflection
    0.5565 = 0.5565
  4. Calculate Shear Stress
    Shear Stress
    29153 = 29153
  5. Calculate Solid Length
    Solid Length
    1 = 1

Engine last updated . Checked against 1 independently-derived test — how we verify calculators. Built by Paul Gunder, a software engineer, not a licensed financial, medical, or legal professional.

Frequently Asked Questions

Why does wire diameter change the spring rate so much more than coil diameter does?

Spring rate is k = Gd⁴/(8D³N), so wire diameter appears to the fourth power while coil diameter only appears cubed (in the denominator). Doubling the wire diameter multiplies stiffness by 16x, while doubling the coil diameter only divides it by 8x. That's why a small increase in wire gauge is by far the most powerful lever for stiffening a spring design.

What does the Wahl factor correct for, and when does it matter most?

The Wahl factor, Kw = (4C−1)/(4C−4) + 0.615/C, adjusts the basic torsion-shear formula for two effects a simple calculation misses: extra direct shear from the coil's curvature and stress concentration on the inside surface of each coil. As the spring index C = D/d drops below about 6, the coil is tightly wound relative to the wire and this correction grows quickly, which is why tightly coiled, small-index springs need it most.

Why does free length add a 15% clash allowance on top of solid length and deflection?

Free length is solid length plus the working deflection plus 15% of that deflection as extra margin. The allowance exists so the spring never fully compresses to solid height (coil-bound) under normal operating load — a spring designed with zero clearance would take all its stiffness abruptly at solid length and risk overload or coil damage the moment the load slightly exceeds the design case.

Why does solid length use active coils plus 2 instead of just the active coil count?

Solid length is (N + 2) × d because the calculator assumes closed-and-ground ends, a common finishing method where the two end coils are squeezed flat against the coil above and below and ground smooth for a flat bearing surface. Those two end coils don't flex and don't contribute to N in the spring-rate formula, but they still take up physical space when the spring is fully compressed.

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