Wire Diameter for Load Formula
Solving the spring rate equation for wire gives d = (8*k*D^3*Na/G)^(1/4) - wire size enters the rate at the fourth power. Use the working spring wire size calculator to solve d from a target rate or load and check the stress it implies.
The fourth-power solve
Rearranging k = G*d^4/(8*D^3*Na):
d = (8*k*D^3*Na / G)^(1/4)
Why wire dominates
Because d enters at the fourth power, a 10% wire increase stiffens the spring ~46% - and also raises the stress capacity faster than the stress.
Check stress next
A wire that hits the rate may still fail the allowable at working load - the working calculator runs both.
Frequently asked questions
Standard wire sizes?
Springs are wound from standard gauge series; round the solved d UP to the next stock size and re-run the rate with the actual wire.
Does load or rate drive the solve?
They are linked by the working deflection: k = F/x. Pick the load point first, then the rate solve gives the wire.
Related pages
- Spring wire size calculator - wire from target rate with stress and travel checks.
- Spring design calculator - wire AND coils from load, travel and index.
- Spring wire properties - G, E and allowables by material.