Guitar String Tension by Mass Calculator

Guitar string tension from linear mass: formula and example

Rearrange Mersenne's law to solve for T and you get T = 4 · L² · f² · μ. The result is in newtons as long as L is in m, f in Hz and μ in kg/m. Take a plain steel high E4 (f = 329.63 Hz) over L = 0.65 m with μ ≈ 0.0007 kg/m: that comes to T ≈ 124 N, about 12.6 kgf. A full steel-string acoustic set pulls roughly 80 kgf (~785 N) on the top, while a nylon classical set lands near 40 kgf (~390 N). That gap is why classical tops are thinner and rely on fan bracing.

Context and applications

Before switching gauges, luthiers work out the per-string tension so they don't warp the neck or split the top. Move from D'Addario EJ16 light (.012-.053, ~74 kgf total) to EJ17 medium (.013-.056, ~88 kgf total) and you add nearly 14 kgf, which is usually enough to call for a truss-rod tweak. Drop tunings like Drop D or D standard pull the tension down and feel slacker. Go up a gauge and the firmness comes back.

FAQ

Why does μ matter more than diameter? Wound strings (the bass ones) have a steel core wrapped in metal, so two strings can share a diameter and still differ a lot in mass. Go by the manufacturer's published unit weight rather than the gauge alone.

What is a safe tension for a classical guitar? Nylon sets come as normal (38-42 kgf), hard (42-46 kgf) or extra-hard (46-50 kgf). Push past 50 kgf and you risk lifting the bridge on an instrument that was built for nylon.

How does scale length change tension? T grows with L². So a 25.5" Fender tuned to E4 needs about 7% more tension than a 24.75" Gibson on the same gauge. It's the reason short-scale basses feel floppy.