String Tension Calculator

This solves Mersenne's law for any stretched string, in SI units. Give it the vibrating length, the frequency, which harmonic that frequency is and the mass per unit length, and it returns the tension in newtons, kilograms force and pounds force, along with the wave speed, the wavelength of that mode and the harmonic series above the fundamental. The second action runs it backwards from a known tension to the pitch and the nearest note, and the third works the mass per unit length out from a material density and a wire diameter before doing either. The equation is exact for an ideal flexible string, so the upper partials of a short thick one will read sharp of the figures given.

Calculator Type
Length In
Mass Per Unit Length In

The string is this long, it sounds this pitch, and a metre of it weighs this much. How hard is it being pulled?

Between the two fixed ends, not the whole string.
1 for the fundamental. Use 2 if you measured the octave above it, and so on.
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Length In
Tension In
Mass Per Unit Length In

The other direction. Pull a string of known weight to a known tension and this is the note it gives, along with everything above it.

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Density In
Diameter In
Length In

For a plain round wire the mass per unit length is just geometry: the density of the material times the cross-sectional area. Give the material and the gauge and this works that out, then the tension it needs for the pitch you want.

Steel is about 7,850 kg/m3, nylon about 1,150, bronze about 8,800, tungsten about 19,300.
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