Compression and Extension Spring Calculator
Estimate geometry, deflection, stiffness, stored energy, and nominal shear stress for close-coiled helical compression or tension springs.
Engineering screening tool—verify inputs and results independently. Use at your own risk.
Spring inputs
Choose the cross-section relation, then enter positive spring dimensions, material stiffness, and axial force.
Calculated response
Minimum free length and pitch are equality-based geometry at the entered force. Add operating clearance and independently check end geometry, preload, buckling, fatigue, and allowable stress.
How to use
- Select Round wire or Rectangular / flat wire. The latter preserves a one-size empirical relation and is not a general width-by-thickness model.
- Enter wire size d and mean coil diameter D in mm, active coil count n, shear modulus G in GPa, and positive axial force magnitude F in N. Compression and extension use the same unsigned elastic relation; hooks and initial tension are not included.
- Select Calculate, or edit a field for an immediate update. Select Reset to restore the round-wire 2 mm, 12 mm, 30-coil, 79.3 GPa, and 100 N example.
- Read deflection, nominal shear stress, stiffness, stored energy, outer diameter, mean radius, closed length, minimum free length, and minimum pitch. Outputs are rounded to two decimals.
- Correct any warning before interpreting results. Do not use this simplified model for end-hook design, initial tension, coil clash, buckling, surge, yielding, relaxation, fatigue-life certification, or safety-critical final design.
Worked example
1. Select Round wire and enter d = 2 mm, D = 12 mm, n = 30, G = 79.3 GPa, and F = 100 N. 2. The calculator gives f = 32.69 mm, τ = 381.97 MPa, k = 3.06 kN/m, W = 1.63 J, Dout = 14.00 mm, Lc = 60.00 mm, L₀,min = 92.69 mm, and smin = 3.09 mm/coil. 3. The substantial deflection and nominal stress require clearance, allowable-stress, and fatigue checks before specifying a spring.
Equations used
Geometry: Dout = D + d; r = D/2
Closed length: Lc = nd
Round-wire deflection: f = 64nr³F/(d⁴G)
Flat-wire deflection: f = 44.9nr³F/(d⁴G)
Round-wire stress: τ = 16Fr/(πd³)
Flat-wire stress: τ = 4.8Fr/d³
Stored energy: W = Ff/2
Stiffness: k = F/f
Minimum free length: L₀,min = Lc + f
Minimum pitch: smin = L₀,min/n
d is round-wire diameter or the flat-wire relation’s characteristic size; D and r are mean coil diameter and radius; n is active-coil count; G is shear modulus; F is positive axial force magnitude; f is deflection; τ is nominal shear stress; W is stored elastic energy for linear loading from zero; k is secant stiffness; and Lc, L₀,min, and smin are solid/equality-based dimensions. The calculator converts mm and GPa to SI internally. Force has no algebraic sign.
Theory and method
A close-coiled helical spring responds mainly through torsion of its wire. The mode-specific compliance and stress coefficients are applied to the mean coil radius. The same unsigned force–deflection relation screens compression and extension loading, but an extension spring’s hooks, transition coils, and initial tension need separate treatment.
Assumptions and limits: homogeneous isotropic material, linear shear elasticity, close coils, concentric axial loading, uniform active turns, and no preload. Curvature/Wahl correction, direct shear, end conditions, initial tension, coil contact clearance, buckling, surge, temperature relaxation, yielding, and fatigue are excluded. The rectangular/flat mode has only one empirical size d and must not be extrapolated as a complete rectangular-section model.
Reference: A. van Beek, Advanced Engineering Design: Lifetime Performance and Reliability, helical spring calculation collection; equations reproduced above. Validate production designs against an applicable spring standard and supplier material/fatigue data.
Continue in TriboSolver to refine stress correction, end geometry, material behavior, contact, and service loading.
