Double the wire, sixteen times the spring rate

A helical spring’s stiffness scales with wire diameter to the fourth power — doubling it multiplies the rate by 16.

Why it works

k = Gd⁴/(8D³n): d appears to the fourth power. A seemingly small jump in wire gauge changes a spring’s feel far more than instinct suggests.

Do it exactly

Estimate with the rule, then check it against the calculator that models it properly.

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More in Mechanical

• The bolt-torque shortcutTightening torque ≈ 0.2 × preload × bolt diameter (dry steel).
• Torque mostly fights frictionRoughly 90% of tightening torque is lost to friction; only ~10% actually stretches the bolt.
• Deflection limits: span/250Keep beam deflection under span/250 generally, span/360 where people will notice a bouncy floor.
• Depth beats width, cubedDouble a beam’s depth and its deflection drops 8-fold. Double its width and it only halves.

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