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Compression spring calculator

Enter the wire, coil diameter, coils and lengths of a round-wire helical compression spring and get the spring rate, the load and Wahl-corrected stress at working length, the solid height and solid stress, the spring index and the surge frequency. Inch (lbf) or metric (N, mm). Free, no sign-up, runs in your browser.

Spring rate

-Load per unit deflection

Load at working length

-Stress - (- of limit)

Solid height

-Clearance to working length -

Results

Mean coil diameter D-
Spring index C = D/d-
Wahl factor Kw-
Total coils-
Working deflection-
Deflection to solid-
Load at solid-
Shear stress at solid-
Estimated tensile strength-
Screening limit (45 %)-
Natural frequency (surge)-

Checks

    How the calculator works

    The calculator treats the spring as a round-wire helical spring with the same pitch along its length, loaded along its axis. It uses the standard textbook formulas for such springs.

    1. Mean diameter and index. D = outside diameter − wire diameter d. The spring index is C = D/d.
    2. Spring rate. k = G·d4 / (8·D3·Na), where G is the shear modulus of the wire and Na the number of active coils. The load at a compressed length is F = k·(free length − compressed length).
    3. Stress. The corrected shear stress is τ = Kw·8·F·D / (π·d3) with the Wahl factor Kw = (4C − 1)/(4C − 4) + 0.615/C.
    4. Total coils and solid height. Closed and ground ends: Nt = Na + 2, Hs = Nt·d. Closed, not ground: Nt = Na + 2, Hs = (Nt + 1)·d. Plain: Nt = Na, Hs = (Nt + 1)·d. Plain and ground: Nt = Na + 1, Hs = Nt·d.
    5. Strength. The tensile strength of the wire is estimated with the common correlation Sut = A/dm (constants depend on the material, d in mm). The screening limit for static loading is 45 % of it, a common rule for the torsional yield strength of spring wire. It is a screening value, not a guarantee: ask the wire supplier for certified strength.
    6. Surge. The natural frequency of the active coils with both ends held is f = ½·√(k/m), with m the mass of the active coils. If the spring is cycled at a frequency close to f or a low multiple of it, coil surge can destroy it; keep the cycle frequency below about one thirteenth of f.

    The shear modulus values used are typical values: music wire 79.3 GPa (11.5 Mpsi), hard drawn 78.6 GPa, oil-tempered, chrome silicon and chrome vanadium 77.2 GPa, stainless 69 GPa. Real wire varies by a few percent, so the calculated rate can differ from a measured one by that amount; springs with a tight rate tolerance are tuned by adjusting the coil count.

    Worked example: 2 mm music wire spring

    Wire d = 2 mm, outside diameter 18 mm, so D = 16 mm and C = 8. With Na = 8, closed and ground ends, free length 50 mm and working length 35 mm: k = 79300·24/(8·163·8) = 4.84 N/mm (27.6 lbf/in). Deflection 15 mm gives F = 72.6 N. Kw = 31/28 + 0.615/8 = 1.184, so τ = 1.184·8·72.6·16/(π·8) = 438 MPa. Solid height = 10·2 = 20 mm, so the spring has 15 mm of clearance at working length; the load at solid is 145 N with a stress of 876 MPa. The estimated tensile strength is 2211/20.145 = 2000 MPa, so the 45 % screening limit is 900 MPa: just OK at solid. The surge frequency is about 349 Hz.

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    Questions

    How do you calculate the spring rate of a compression spring?

    Spring rate k = G·d⁴ / (8·D³·Na), where G is the shear modulus of the wire, d the wire diameter, D the mean coil diameter (outside diameter minus wire diameter) and Na the number of active coils. Example: music wire (G = 79.3 GPa), d = 2 mm, D = 16 mm, Na = 8 gives k = 4.84 N/mm (27.6 lbf/in).

    What is the Wahl correction factor?

    The Wahl factor Kw = (4C − 1)/(4C − 4) + 0.615/C, with spring index C = D/d, corrects the simple torsion stress 8FD/(πd³) for the direct shear and the curvature of the wire. Multiply the simple stress by Kw to get the maximum shear stress at the inside of the coil.

    What is a good spring index?

    Most compression springs are made with C between about 4 and 12. Below 4 the coiling is difficult and the stress is high; above 12 the spring tangles easily and is unstable in manufacturing.

    How do I calculate solid height?

    It depends on the end type. Closed and ground ends: solid height = (Na + 2)·d. Closed, not ground: (Na + 3)·d. Plain ends: (Na + 1)·d. Plain and ground: (Na + 1)·d. The spring must never be asked to go to solid in service; keep a clearance of at least 10 percent of the working deflection.

    Does this calculator check fatigue life?

    No. It checks static loading: the stress at working length and at solid against a screening limit of 45 percent of the estimated tensile strength of the wire. Springs that cycle many times need a fatigue analysis (for example a Goodman or Zimmerli approach) and shot peening, which this calculator does not do.

    Engineering aid for guidance. Static checks only; it does not check fatigue, buckling in detail, set removal, temperature effects or special end geometry. Verify critical springs with your spring maker and the relevant standard (for example EN 13906-1 or SMI handbook rules); you remain responsible for the design. Nothing you enter leaves your browser except through a share link you copy yourself.