How this instrument works
A vibrating string's pitch depends on three things pulling against each other: how tightly it's stretched (tension), how long the vibrating portion is (scale length), and how much mass it has per unit of length (unit weight — a function of the string's gauge and material). String manufacturers publish unit-weight values for every gauge and material they sell specifically so this relationship can run in reverse: instead of measuring tension directly, you can calculate the tension a given string will settle at once tuned to a target pitch on a given scale length.
The formula itself comes from the physics of a vibrating string under tension, rearranged to solve for tension given frequency, length, and mass per length, with a constant (roughly 386 — the gravitational conversion between mass and weight in inch-pound units) folded in so the result comes out directly in pounds-force. Doubling the scale length quadruples the required tension for the same pitch, since length enters the formula squared, which is part of why a baritone guitar's longer scale needs meaningfully different string gauges than a standard-scale guitar to land at a comfortable tension.
This calculation is the same family of formula behind published string tension charts from manufacturers like D'Addario, which use their own published unit-weight values and a similar gravitational constant — plugging a specific string's published unit weight into this formula at your instrument's actual scale length and tuning closely reproduces those tension figures, which is useful both for choosing new strings and for understanding why an alternate tuning or a capo changes how a guitar feels under the fingers.
- Enter the target pitch as a frequency in Hz (for example, 329.63 Hz for a standard-tuned high E string).
- Enter the scale length in inches — the vibrating string length from nut to bridge saddle.
- Enter the string's unit weight in pounds per inch, taken from the string manufacturer's published gauge chart.
- Read the resulting tension in both pounds-force (lbf) and newtons (N).
Worked example — a standard-tuned high E string
A plain steel .010-inch high E string (E4, 329.63 Hz), on a 25.5-inch scale length typical of a Fender or Gibson-style guitar, has a manufacturer-published unit weight of 0.00002215 lb/in. Squaring the frequency-and-length term: (329.63 × 2 × 25.5)² = 16,811.13² ≈ 282,614,092.
Multiplying by unit weight over the gravitational constant: 282,614,092 × (0.00002215 ÷ 386.088) ≈ 16.214 lbf — a typical tension for a plain .010 high E string at standard pitch on this scale length. Converted to metric, that's 16.214 × 4.44822 ≈ 72.122 newtons.
Questions
Why does doubling the scale length quadruple the tension?
Because scale length enters the tension formula squared, not linearly — the formula multiplies frequency by 2 times scale length, then squares that whole product. Doubling scale length while holding pitch and unit weight fixed doubles that inner term, and squaring a doubled value quadruples the result, which is why longer-scale instruments like baritone guitars or basses need meaningfully different string gauges to reach comfortable tensions.
Where do I find a string's unit weight?
String manufacturers publish unit-weight values (in pounds per linear inch) for every gauge and material combination they sell, usually in a tension chart or technical reference on their website — D'Addario's is a commonly cited example. It's not something you typically measure yourself; it's a published physical property of that specific string.
Why does the formula divide by 386.088 specifically?
That number is the gravitational conversion constant in inch-per-second-squared units (32.174 ft/s² converted to inches by multiplying by 12), needed because the formula mixes mass-like quantities (unit weight, essentially mass per length) with a force-like result (tension in pounds-force). Some published tension charts round this constant slightly differently (386.4 is also common), which shifts results by a fraction of a percent, but it never varies by string or instrument.
Does higher tension always mean a 'better' feeling string?
No — tension preference is largely about playing feel, not a fixed target to maximize. Lower-tension strings feel looser and are easier to bend but can feel floppy or buzz more; higher-tension strings feel firmer and more resistant but can be more tiring to fret and bend. Most players settle on a tension range that suits their playing style rather than chasing a single 'correct' number.
How does tuning down (like drop D) affect string tension?
Lowering the target pitch reduces tension directly, since frequency enters the formula squared just like scale length does — tuning a string down a whole step roughly halves its tension for the same gauge and scale length, which is exactly why heavier gauges are often recommended for down-tuned guitars: they restore some of the tension and playing feel lost by lowering the pitch.