Helical Spring Calculator

Spring shear stress is Kw·8PD/πd³: 1000 N on a 10 mm wire coiled at 80 mm mean diameter gives τ = 241.206 MPa and a deflection of 51.2 mm.

Axial load P (N):

Wire diameter d (mm):

Mean coil diameter D (mm):

Active coils n:

Modulus of rigidity G (GPa):

Maximum shear stress τ (Wahl) =

241.2061371819 MPa

Precision

Full answer, then cut to fewer decimals (not rounded):

241.2061371819 MPa
241.206137181 MPa
241.20613718 MPa
241.2061371 MPa
241.206137 MPa
241.20613 MPa
241.2061 MPa
241.206 MPa
241.20 MPa
241.2 MPa

Deflection δ = 8PD³n/Gd⁴: 51.2 mm
Stiffness k = Gd⁴/8D³n: 19.5313 N/mm
Spring index C = D/d: 8
Wahl factor Kw: 1.18402
Shear stress without curvature 8PD/πd³: 203.718 MPa
Energy stored ½Pδ: 25.6 J

Step-by-step solution

C = 80 ÷ 10 = 8
Kw = (4C − 1)/(4C − 4) + 0.615/C = 1.18402
τ = Kw × 8PD/πd³ = 1.18402 × 203.718 = 241.206 MPa
δ = 8PD³n/Gd⁴ = 51.2 mm

Helical Spring Formula

τ = Kw 8PD/πd³, δ = 8PD³n/Gd⁴

Kw = (4C − 1)/(4C − 4) + 0.615/C, C = D/d

Worked Example

A spring with d = 10 mm, D = 80 mm, 10 active coils and G = 80 GPa under 1000 N:

C = 80 ÷ 10 = 8
Kw = (4C − 1)/(4C − 4) + 0.615/C = 1.18402
τ = Kw × 8PD/πd³ = 1.18402 × 203.718 = 241.206 MPa
δ = 8PD³n/Gd⁴ = 51.2 mm

Stiffness k = Gd⁴/8D³n: 19.5313 N/mm · Spring index C = D/d: 8 · Wahl factor Kw: 1.18402 · Shear stress without curvature 8PD/πd³: 203.718 MPa · Energy stored ½Pδ: 25.6 J

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Frequently asked questions

What does the Wahl factor correct for?

Direct shear and the higher stress on the inside of the curved wire; it is larger for small spring indices C = D/d.

How do springs in series and parallel combine?

In series 1/k = 1/k₁ + 1/k₂; in parallel k = k₁ + k₂.

Sources

Last reviewed: 2026-10-15. Factors are stored exactly and computed with 50-digit decimal arithmetic. See how we verify conversion factors.

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APA

Scientific Converters. (2026, October 15). Helical Spring Calculator. Retrieved October 25, 2026, from https://scientificconverters.com/calculators/helical-spring-calculator/

IEEE

Scientific Converters, "Helical Spring Calculator," scientificconverters.com. Accessed: Oct. 25, 2026. [Online]. Available: https://scientificconverters.com/calculators/helical-spring-calculator/