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String Tension and Scale Length Calculator
Music knowledge / Guides and practical tools
About this reference
From the music-learning collection, adapted for Philojain Music Muse. Referenced sources remain credited in the article.
Tension is what a string feels like under the hand, and it follows from three things: how heavy the string is, how long it is, and how high it is tuned. Enter those and this gives the tension — and shows what changes if you move any one of them.
The calculator
Unit weight is printed by the string manufacturer for every gauge; read yours off the packet rather than trusting a number here. This page carries no gauge table, because a table would be a claim about your strings it has no way to check.
The three variables, and how they trade
Tension rises with the square of both the scale length and the pitch, and linearly with the weight of the string. That asymmetry is the whole practical story: dropping a string by an octave takes three quarters of its tension away, and no reasonable change of gauge fully replaces it — whereas a longer scale gets some of it back, because the length term is squared as well.
Reading the unit weight
Unit weight is mass per unit length, and string manufacturers publish it per gauge and per construction. Two strings of the same nominal gauge can differ, because a wound string’s core-to-wrap ratio changes how much of its mass actually vibrates. Use the figure for the strings in your hand.
What the measurements actually say
The relationship underneath this calculator was published by Marin Mersenne in Traité de l’harmonie universelle in 1637, and was the first experimentally proven statement of it: ƒ = (1 / 2L) √(T / μ). Frequency falls with vibrating length, rises with the square root of tension, and falls with the square root of mass per unit length. Nearly every tuning decision is that one equation solved for a different variable.
The measured figure most players find counter-intuitive concerns which string is tightest. D’Addario Pro Steels on a 34-inch bass measure G 41.9 lb, D 47.4 lb, A 44.9 lb and E 37.3 lb. The low E is the slackest string on the instrument, not the tightest. That — and not its thickness — is why low strings feel floppy: manufacturers do not scale gauge up far enough to hold tension constant across the set. A deliberately balanced set fixes it, landing all five strings inside a four-pound spread. Verified — manufacturer tension chart.
One widely repeated figure about extended-range instruments is out by an octave. The eight-string guitar’s lowest string is published by more than one well-read outlet as “F♯0, 23 Hz”. The correct value is F♯1 ≈ 46.25 Hz, which sits above a four-string bass low E at 41.20 Hz. A nine-string’s low C♯ at 34.65 Hz likewise sits above a five-string bass low B. An eight-string guitar has not gone below the bass, and a tension calculation that assumes it has will be wrong by a factor of two in frequency and four in tension.
How these figures are graded. Each is marked verified where it comes from a manufacturer datasheet or a published component-level measurement, practitioner consensus where credentialed builders agree but no measurement was found, and unverified where a claim is repeated widely and traceable nowhere. Where a figure could not be sourced it is said so rather than quietly omitted.
What it does not do
It gives static tension, not feel. How a string plays also depends on the action, the neck relief, the break angle behind the nut and saddle, and how much string there is beyond the speaking length — none of which is in this arithmetic. Two setups at the same computed tension can feel quite different, and the number is a starting point rather than a verdict.
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