Compression Spring Design Calculator

How it works

A helical compression spring loads its wire in torsion. The rate depends on the wire stiffness, the fourth power of the wire diameter, the cube of the coil diameter and the number of active coils.

k = G d⁴ ÷ (8 D³ N_a), τ = K_w × 8 F D ÷ (π d³), K_w = (4C − 1) ÷ (4C − 4) + 0.615 ÷ C

The tensile strength of spring wire falls with diameter: S_ut = A ÷ d^m, with constants for each wire material (Shigley, Table 10-4). The allowable static shear stress is taken as 45 percent of S_ut for carbon and alloy steel and 35 percent for stainless steel and bronze (not preset). The calculator also reports the stress at solid height (all coils touching), a buckling check for ends fixed and guided, and the surge frequency, below which the coils can resonate. See Structures and Strength of Materials and Gears and Power Transmission for the surrounding ideas.

Worked example

A music-wire spring: wire 2.0 mm, mean diameter 16 mm, 8 active coils, squared and ground ends, free length 60 mm, working load 100 N.

• k = 81 700 × 2⁴ ÷ (8 × 16³ × 8) = 4.99 N/mm, so the deflection at 100 N is 20.1 mm and the length under load 39.9 mm.
• C = 16 ÷ 2 = 8 and K_w = 31 ÷ 28 + 0.615 ÷ 8 = 1.184. τ = 1.184 × 8 × 100 × 16 ÷ (π × 2³) = 603 MPa.
• S_ut = 2 211 ÷ 2^0.145 = 2 000 MPa; the allowable static stress is 0.45 × S_ut = 900 MPa, so the working stress is 67 % of it.
• Total coils N_t = 10, solid height 10 × 2 = 20 mm. At solid (40 mm of travel) the load is 199 N and the stress 1 203 MPa (60 % of S_ut).
• Surge frequency = ½ √(k ÷ m) = 355 Hz: the spring is not suitable for cycling near that frequency or its multiples.

Things to know

This is a static design check. For springs that cycle, a fatigue analysis (Goodman or Gerber with the shear stress range) is needed: the allowable stress then falls to a fraction of the static value, and shot peening helps.

Pre-setting (compressing the spring to solid at manufacture) allows higher stress at the working load, but changes the free length. Say so on the drawing.

The strength constants (A and m) are typical for the wire sizes of the standard tables (about 0.3 to 12 mm). Check the supplier’s data for exact grades.

Keep the spring index between about 4 and 12: low indices are hard to coil and have high stress concentration, high indices tangle and buckle.

Maintain at least 10 to 15 percent of the working deflection as clearance between working length and solid height.

A spring that fits in a hole or over a pin needs clearance for its diameter change under load: the outside diameter grows slightly as the spring compresses.

Common questions

What is the spring rate?

The force needed to deflect the spring by one unit of length, in N/mm or lbf/in. Springs in parallel add their rates; springs in series combine as 1 ÷ k = Σ 1 ÷ k_i.

What is the Wahl factor?

A correction to the simple torsion stress formula for the curvature of the coils and the direct shear of the wire. It raises the stress on the inside of the coil, by about 18 percent for a spring index of 8.

Why does a spring buckle?

A long, slender compression spring behaves like a column. The risk rises with the ratio of free length to coil diameter and with the end conditions: guide it on a rod or in a bore, or shorten it.

How many active coils are there?

The coils that actually deflect. The end coils of a squared spring rest against the seat and do not count: for squared and ground ends the total is Na + 2.

Sources

• Budynas, R. G. and Nisbett, J. K., Shigley’s Mechanical Engineering Design, McGraw-Hill, Chapter 10 (springs: Tables 10-1, 10-4, 10-6, Eq. 10-13, 10-25).
• Spring Manufacturers Institute, Handbook of Spring Design; ASTM A228, A229, A227, A313, B159 (wire specifications).

Last reviewed: November 2, 2026