Violin String Tension Calculator

Violin string tension from linear mass: formula and example

Mersenne's law gives us T = 4 · L² · f² · μ. A 4/4 violin tunes in fifths (G3 = 196 Hz, D4 = 293.66 Hz, A4 = 440 Hz, E5 = 659.25 Hz) over a vibrating length of about L ≈ 0.325 m. Take a typical A4 string with μ ≈ 0.00045 kg/m and the tension comes out near 55 N, or roughly 5.6 kgf. Add up all four and the full set pulls roughly 25-30 kgf (~245-295 N) against the top, with the soundpost and bass bar carrying that load. The bow itself holds about 150-200 strands of horse hair, 6-7 g worth, tensioned by the screw and rosined with cake rosin.

Context and applications

Luthiers nudge the soundpost (alma) around to balance tension against tone. Shift it 1 mm toward the bridge and the E brightens while the G goes darker. String size matters for students too. A 3/4 violin runs L ≈ 0.30 m and a 1/2 runs L ≈ 0.27 m, so the same notes need lower tension and lighter strings. Synthetic-core sets like Dominant or Evah Pirazzi land near 23-26 kgf total; pure-gut sets sit lower, around 18-20 kgf, and feel softer under the bow.

FAQ

Why is the E string steel and not gut? At 659 Hz over 0.325 m, gut would have to be so thin it snaps under tension. A plain steel E (μ ≈ 0.00025 kg/m) holds about 80 N, roughly 8.2 kgf, without drama.

Does tuning to A=442 change tension much? Tension scales with f², so going from 440 to 442 Hz adds about 0.9%. That's tiny on a single string, but across the whole set it works out to roughly 250 g of extra pull, and the bridge feels it over time.

How tight should the bow hair be? Tight enough that the stick keeps a slight concave camber while you play. A pencil's width of gap between hair and stick at the middle is the usual rule of thumb. Crank it past that and you warp the stick for good.