String Tension Calculator
Work out how hard a string pulls at a given pitch: unit weight, scale length and frequency give the tension in pounds, kilograms and newtons, plus the plain-steel gauge that would reach that weight.
Plain-steel gauges
| Gauge (in) | Unit weight (g/m) | Tension (lb) |
|---|
Frequency follows the note: A4 is 440 Hz and each semitone multiplies it by 21/12, so E4 is 329.63 Hz. Tension is T = 4μL²f², where μ is the string's mass per metre in kilograms, L the scale length in metres and f the frequency in hertz — 0.398 g/m at E4 over 25.5 in comes to 72.6 N, or 16.31 lb. The gauge table runs the other way for a solid plain-steel string at 7.85 g/cm³, taking μ = (π/4)d²ρ; a wound string carries wrap as well as core, so its mass per metre is higher than a solid string of the same diameter and you should use the maker's published unit weight for those. Tension rises with the square of frequency, so the same string tuned up a semitone gains about 12%, and a longer scale or a heavier string raises it in proportion. Everything runs locally in your browser with no storage, uploads or network access.