Understanding guitar string tension
When a string is tuned to pitch, it is stretched tight enough that plucking it produces a specific fundamental frequency. The force doing that stretching is the string's tension, and it depends on four things: how heavy the string is per inch of length (its unit weight), how long the vibrating portion is (the scale length), and how fast it needs to vibrate (the frequency of the target note). This calculator applies the same physics used by string manufacturers to publish their tension charts.
The formula
The fundamental frequency of a vibrating string follows f = (1 / 2L) x sqrt(T / UW). Solving for tension gives the form used here, in pounds-force with lengths in inches and frequency in Hz:
- T = UW x (2 x L x f)^2 / 386.4
- T is string tension, in pounds-force (lbs).
- UW is unit weight — the string's mass per inch of length, in lb/in.
- L is scale length — the vibrating length of the string, in inches.
- f is the target frequency of the note, in Hz.
- 386.4 is the acceleration due to gravity in in/s², used to convert a mass-based unit weight into a force in the inch-pound system.
Getting unit weight from diameter and material
For a plain (solid, unwound) string, unit weight is simply the cross-sectional area times the material's density: UW = density x pi x (diameter / 2)^2. This calculator uses standard densities of 0.283 lb/in³ for plain steel and 0.0412 lb/in³ for nylon. This approach is accurate for plain strings (typically the higher-pitched strings on a steel-string guitar, or trebles on a classical guitar). Wound strings — a metal winding wrapped around a core — do not have a uniform solid density, so treating them as solid wire of the same diameter is an approximation; for exact figures on wound strings, use the unit weight a manufacturer publishes for that specific string.
Common reference points
- Standard scale length: most electric guitars use 24.75" (Gibson-style) to 25.5" (Fender-style); classical guitars commonly use about 25.6" (650 mm); many acoustics use 25.4"–25.5".
- Standard concert pitch: A4 = 440 Hz. In standard guitar tuning, open strings run E2 (82.41 Hz), A2 (110.00 Hz), D3 (146.83 Hz), G3 (196.00 Hz), B3 (246.94 Hz), and E4 (329.63 Hz).
- Typical single-string tension: steel-string guitars are usually set up so each string sits roughly in the 12–20 lb (53–89 N) range; classical nylon-string guitars typically run somewhat lower, often 7–17 lbs depending on the string.
Why tension matters
Total tension across all strings determines how much force pulls on the neck and bridge, which affects setup, intonation, and long-term stability. A heavier gauge or a higher-pitched string tuned to the same note both raise tension; a longer scale length raises tension for the same pitch and gauge (which is why baritone guitars use longer necks). Players also choose gauges partly by feel — higher tension feels stiffer under the fingers, lower tension feels slinkier but can buzz or go out of tune more easily.