Wire material
mm
mm
mm
coils
Ends
mm
mm
Spring compressing between installed and working length
Spring rate, force at any length, shear stress against the wire's limit, solid length, buckling and surge frequency for helical compression springs. Pick the wire material and end type, and see the spring compress to scale.
Force and stress at each length. Allowable stress is the static limit for this wire with set not removed.
| Length | Travel | Force | Stress | % limit |
|---|
| Wire d | Coils n | Solid | C | % limit |
|---|
The spring is a coiled torsion bar: compressing it twists the wire. The rate depends strongly on the wire diameter (4th power) and the coil diameter (3rd power).
End types (active coils n, solid length Ls): closed and ground n = Nt − 2, Ls = Nt·d; closed not ground n = Nt − 2, Ls = (Nt + 1)·d; plain open n = Nt, Ls = (Nt + 1)·d; plain ground n = Nt − 1, Ls = Nt·d. Keep at least 15 % of the travel between working length and solid (fractional overrun), and an index C between 4 and 12 so the spring is easy to coil. Material constants follow Shigley's Mechanical Engineering Design (tables 10-4, 10-5, 10-6) and EN 13906-1.
This calculator designs and checks a helical compression spring made of round wire. Enter the wire diameter, outer diameter, free length, total coils, end type and material, plus the working and preload lengths. It returns the spring rate, the force and shear stress at each length, solid length, spring index, surge frequency and a buckling check, with a table for hitting a target rate. Mechanical designers, product engineers, repair technicians, makers and students use it to specify a spring or to identify one they already have.
The spring has a rate of 3.47 N/mm and gives 52 N at 35 mm, at only 38% of the allowable stress. It is solid-safe, so it will not take a permanent set even if fully compressed, and it uses 50% of the available travel.
For a helical compression spring, k = G × d⁴ / (8 × D³ × n), where G is the shear modulus of the wire (about 81,000 MPa for music wire, 69,000 MPa for 302 stainless), d the wire diameter, D the mean coil diameter (outer diameter minus wire diameter) and n the number of active coils. With d = 1.5 mm, D = 12 mm, n = 6 and music wire, k = 81,000 × 5.06 / (8 × 1728 × 6) = 4.94 N/mm. Multiply N/mm by 5.71 to get lbf/in.
Active coils are the ones free to deflect, and the count depends on the end type. Closed and ground ends, or closed but not ground: n = total coils − 2. Plain open ends: n = total coils. Plain ground ends: n = total coils − 1. A 10-coil spring with closed and ground ends has 8 active coils. Only active coils appear in the spring rate formula, so using the total count gives a rate that is too low.
The spring index is C = D / d, mean coil diameter over wire diameter. It describes how tightly the wire is bent. Aim for 4 to 12. Below about 4 the spring is hard to coil and the stress on the inside of each coil rises sharply. Above about 12 the spring tends to tangle, buckle, and vary in diameter. The index also sets the stress correction factor, so a low index raises the stress for the same force.
Solid length is the height when all coils touch. For closed and ground or plain ground ends, Ls = total coils × wire diameter. For closed (not ground) or plain open ends, Ls = (total coils + 1) × wire diameter. A 10-coil spring of 2 mm wire with ground ends is 20 mm solid. Keep the working length at least 15% of the available travel above solid, since the rate rises and coils clash near solid.
The wire is loaded in torsion, so τ = K × 8 × F × D / (π × d³), with force F, mean diameter D and wire diameter d. K corrects for coil curvature and direct shear. The Bergsträsser factor KB = (4C + 2) / (4C − 3), used in EN 13906-1 and close to the Wahl factor, gives 1.152 at C = 9. Compare τ with the allowable shear, about 45% of tensile strength for music wire and 50% for chrome silicon.
Springs in parallel, side by side and sharing the load, add their rates: k = k₁ + k₂. Two 5 N/mm springs in parallel give 10 N/mm. Springs in series, stacked end to end, add their flexibilities: 1/k = 1/k₁ + 1/k₂. Two 5 N/mm springs in series give 2.5 N/mm, with each carrying the full force. A spring cut in half doubles its rate, because the rate is inversely proportional to the number of active coils.