Guitar String Gauge for Target Tension Calculator
Find the plain-steel string gauge that gives the tension you want at a given note and scale length — the reverse of a tension calculator, for building custom string sets.
How it works
Mersenne / Taylor: T = UW × (2 × L × f)² ÷ 386.4 · rearranged: UW = T × 386.4 ÷ (2 L f)² · plain-steel diameter d = 2 × √(UW ÷ (π × 0.284)), with UW the unit weight in lb/in, L the scale in inches and f the pitch in Hz
A string's tension depends on its unit weight, the scale length and the pitch you tune it to. Standard tension calculators take a known gauge and give the tension; this one runs the physics backwards — you name the tension you want and the note, and it returns the plain-steel gauge that delivers it. That is exactly what you need when building a custom or balanced set: pick a comfortable tension for each string, solve for the gauge, and the whole set feels even under the fingers instead of some strings feeling floppy and others stiff.
Worked example
For 16 lb on a 25.5 in scale tuned to high E (329.63 Hz): (2 × 25.5 × 329.63)² ≈ 2.826 × 10⁸, so unit weight = 16 × 386.4 ÷ 2.826 × 10⁸ ≈ 2.19 × 10⁻⁵ lb/in. A plain steel string of that unit weight has a diameter of 2 × √(2.19 × 10⁻⁵ ÷ (π × 0.284)) ≈ 0.0099 in — a standard .010 gauge.
Frequently asked questions
Why would I compute gauge from tension instead of the other way round?
Because comfort and feel come from tension, not gauge. Building a "balanced tension" set means choosing a tension you like for each string and then solving for the gauge that produces it, so no string feels floppier or stiffer than its neighbours.
Does this work for wound strings?
It solves for a plain (solid) steel core, which is accurate for the plain treble strings. Wound strings pack extra mass into a thin core, so their true gauge is larger than a solid steel string of the same unit weight — use the unit-weight figure and the manufacturer's wound-string data for those.
What is the 386.4 in the formula?
It is the acceleration of gravity expressed in inches per second squared (386.4 in/s²), which converts the mass-based tension formula into the pound-force and inch units used for strings.
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This calculator is for educational purposes. Double-check important results before acting on them.