Helical Compression Spring Rate Calculator
Spring rate (stiffness) of a helical coil spring from wire diameter, mean coil diameter, active coils and material — load and stress at a given deflection, spring index, solid height and natural frequency.
How it works
k = G d⁴ ÷ (8 D³ n) (D = mean coil diameter); τ = Kw × 8 F D ÷ (π d³), Kw = (4C − 1)/(4C − 4) + 0.615/C, C = D/d; solid height ≈ (n + 2) d
A compression spring is a torsion bar wound into a helix, and its stiffness follows from the shear modulus of the wire and the geometry: rate rises with the fourth power of wire diameter, so a 10% thicker wire is 46% stiffer, and falls with the cube of coil diameter and in proportion to the number of active coils. The stress in the wire is torsional shear, boosted on the inside of the coil by curvature (the Wahl factor), and it must stay under about 45% of the wire’s tensile strength for a static spring — much less for fatigue. The spring index D/d should sit between 4 and 12 for manufacturability. Solid height limits travel, and a spring cycled near its natural frequency surges, so designers keep operating frequency well below it.
Worked example
3 mm music wire, 24 mm outer diameter (21 mm mean), 8 active coils: rate 10.84 N/mm (61.9 lbf/in). At 20 mm deflection it carries 217 N with 521 MPa of Wahl-corrected shear stress — below the ~810 MPa static allowable — and its solid height is 30 mm, exactly the travel a 60 mm free length allows.
Frequently asked questions
How do I count active coils?
Total coils minus the end coils that sit flat on the seat: subtract 2 for squared-and-ground ends, 1 for plain-ground, 0 for plain open ends.
What about extension or torsion springs?
Extension springs use the same rate formula plus initial tension; torsion springs bend the wire and use E instead of G: rate (N·mm/turn) = E d⁴ ÷ (64 D n × 180/π).
Related calculators
Engineering estimate for education and preliminary design. Use manufacturer data, applicable standards and appropriate safety factors, and have critical designs checked by a qualified engineer.