Calculate geometry, forces and stresses of a cylindrical helical compression spring to EN 13906-1.
Calculate rate, stresses and geometry of a cold-formed helical compression spring.
Wire diameter d, mean coil diameter D, active coils n, free length L₀, end type and material data define the spring. Two working deflections or forces describe the operating range.
Spring index D/d affects manufacturability and curvature stress. Free length and solid height bound usable travel; material and surface condition determine whether stress is acceptable for static or cyclic duty.
Rate follows from shear modulus, wire diameter, mean coil diameter and active coils. Spring index w = D/d indicates manufacturability; shear stress includes curvature and Wahl effects.
d = 2 mm, D = 20 mm and n = 8 give w = 10, a common starting value. Solid height from total coils must remain below the shortest working length.
Sources and limits: EN 13906-1 covers calculation and checks for cylindrical compression springs; material data commonly follows EN 10270. Check dynamics, buckling and set separately.
Calculate rate, stresses and geometry of a cold-formed helical compression spring.
Wire diameter d and mean coil diameter D describe the spring body; their ratio w = D/d affects curvature correction and manufacturability. Only active coils n enter the spring rate. Free length L0 instead describes unloaded installation space and, together with solid height Lc, limits available travel. EN 13906-1 treats these quantities separately because equal envelope dimensions do not imply equal force, stress or buckling resistance.
Rate follows from shear modulus, wire diameter, mean coil diameter and active coils. Spring index w = D/d indicates manufacturability; shear stress includes curvature and Wahl effects.
| Symbol / input | Meaning |
|---|---|
| d | Wire diameter; it affects rate to the fourth power and stress to the third power. |
| D | Mean coil diameter measured from wire centre to wire centre; do not confuse it with outside or inside diameter. |
| n | Number of active coils; closed end coils do not contribute fully to elastic deflection. |
| L0, Lc | Unloaded free length and solid height with touching coils; their difference limits total geometric travel. |
| s1, s2 | Working deflections from free length, paired with calculated forces F1 and F2. |
| R | Spring rate in N/mm: additional spring force per millimetre of travel in the linear range. |
Wire diameter d, mean coil diameter D, active coils n, free length L₀, end type and material data define the spring. Two working deflections or forces describe the operating range. Spring index D/d affects manufacturability and curvature stress. Free length and solid height bound usable travel; material and surface condition determine whether stress is acceptable for static or cyclic duty.
Enter wire diameter d, mean coil diameter D, number of active coils, free length and material data. Also provide two working deflections or forces to check rate and stress within the actually used range.
d = 2 mm, D = 20 mm and n = 8 give w = 10, a common starting value. Solid height from total coils must remain below the shortest working length.
Spring rate R is the slope of the idealized linear force-deflection curve; F1 and F2 are the forces at entered working deflections s1 and s2. Corrected shear stress accounts for the higher stress at the inside of the curved wire. Clearance to solid indicates geometric travel reserve only. A long slender spring may buckle first; EN 13906-1 therefore treats buckling as a separate verification and may require a mandrel or sleeve guide.
Diameter in millimetres, rate in N/mm, force in N, stress in MPa.
Designing a new compression spring for a known force-deflection range, or checking whether an existing spring's geometry delivers the required force within allowable stress.
EN 13906-1 covers calculation and checks for cylindrical compression springs; material data commonly follows EN 10270. Check dynamics, buckling and set separately.
Common mistake: Don't ignore spring index D/d – values below about 4 are considered hard to manufacture, and above about 20 prone to buckling and guidance issues. Solid height (all coils compressed) must stay below the shortest intended installed length, or the spring bottoms out before reaching the intended travel.
Values between about 4 and 12 are considered easy to manufacture and mechanically favorable; smaller values complicate winding, larger values favor buckling and uneven stress distribution.
Real shear stress is higher at the wire's inner side than the ideal value because of wire curvature and transverse force; Wahl or curvature factors correct for this and matter especially at low spring index.
Once all coils touch, the spring can no longer absorb further travel and force rises abruptly; solid height must therefore stay below the shortest operating length.
No. Rate uses the number of active coils. Closed or ground end coils transfer load and increase total coil count or solid height, but do not act as fully active coils.
No. The force and stress calculation does not replace the separate EN 13906-1 buckling check, especially for a large free-length-to-diameter ratio. Springs that are not buckle-resistant require suitable guidance.
Wire, coil, and length geometry plus two deflections produce spring forces, stresses, work, and stability indicators.
The calculator covers cold-formed cylindrical compression springs made from round wire. Stability, dynamics, and relaxation belong alongside the force curve.
Slender springs can require internal or external guidance depending on installed length.
For rapid cycling, two static working points are insufficient; check surge and impact.
Long-term force loss depends strongly on material, stress, and service temperature.
Material and delivery requirements for common spring wires.
Use the extended stress, buckling, and relaxation checks for dynamic applications.
Requirements for shot-peened compression springs where fatigue matters.