Guide
String tension from scale length, pitch and gauge: T = μ × (2Lf)²
When you change string gauges or tune down, the feel changes and the neck can move. The reason is tension, the pull of each string along its length, which can be calculated from three things: how heavy the string is, how long its vibrating length is and what pitch it is tuned to. This calculator does that for each string of a set and adds up the total, in pounds, kilograms and newtons.
The formula
Mersenne’s law for a vibrating string says T = μ × (2 × L × f)², where μ is the mass per unit length of the string, L is the vibrating length, the scale length, and f the frequency. Doubling the frequency quadruples the tension; doubling the weight doubles it. For a plain steel string, μ is the density of music wire, 7,850 kg per cubic metre, times the cross-section of a circle of the gauge you enter. Wound strings have wire wrapped around a core, so their weight cannot be found from the gauge, and the tool asks for the unit weight printed in the string maker’s tension chart.
A worked example
Press Sample: a scale length of 25.5 inches, as on a Stratocaster, with a plain .010 string tuned to E4, a .013 to B3 and a .017 to G3. The E4 string at 329.63 Hz pulls 16.30 lb, which is 7.40 kg or 72.5 N. The B3 string is 15.46 lb and the G3 string 16.66 lb. The total of the three is 48.4 lb, or 22.0 kg. Change the scale length to 24.75 inches, as on a Les Paul, and the E4 string falls to 15.36 lb. Tune the whole set down two semitones and the .010 string drops to 12.94 lb.
Choosing scale length
Longer scales need more tension for the same pitch and gauge, which gives a tighter feel and clearer attack. The chips set 25.5″ and 24.75″ for electric guitars, 25″ for many acoustics, 34″ for a bass, and shorter lengths for a ukulele or small instruments. Measure from the nut to the 12th fret and double it if you are not sure of the scale.
Tuning down and changing gauge
Tension changes with the square of the frequency. A whole step down, two semitones, reduces the frequency by about 11 percent and the tension by about 21 percent. That is why strings feel loose when dropped, and why players move to a heavier gauge to keep the same feel. To find a gauge that restores the tension, change the gauge until the pounds match the original.
Wound strings
Enter the unit weight in pounds per inch. It is printed in the tension charts from companies that make strings, for example a figure with several digits after the decimal point. If it is blank the string is left out of the total and the page says so. Different makers use different alloys and winding, so the same nominal gauge can have a different weight.
Edge cases
Real strings differ from the ideal by around a percent because of alloy and tolerance. The result is for an open string at pitch; fretting a note raises the tension a little, and bending raises it more. Stiffness of thick strings, especially on short scales, makes the pitch a bit sharp. The note menu runs from E1 to E5 for each string.
Limits
The calculator gives a pull, not a verdict on whether your instrument can take it. Truss rods, bridges and necks differ, so check against the maker’s guidance. Settings are saved in your browser.
Related tools
- Note Frequency Chart shows the pitch each string has to reach in hertz.
- Online Tuner helps you reach the pitch safely.
- Fretboard Trainer teaches the note names along the neck.
- Ukulele Chord Finder shows chord shapes once the strings are on.
Checked against the current version of the Guitar String Tension Calculator on .