How to use the guitar string tension calculator
- Enter the scale length (the vibrating length from nut to saddle) and choose inches or millimeters.
- For each string, enter its note such as E2 or F#3, and either a plain steel gauge in inches or a unit weight from the maker's chart.
- Read the tension of each string in pounds, kilograms and newtons, and the total for the set.
- Open the advanced options to change the reference pitch of A4 or the steel density.
Formula
Tension T = mu x (2 L f)^2
mu = mass per length, L = vibrating length, f = pitch in hertz
Plain steel: mu = (pi / 4) x diameter^2 x density
Pitch of a note from equal temperament: f = A4 x 2^((n - 69) / 12), n = MIDI note number
In pounds: T = unit weight (lb/in) x (2 L f)^2 / 386.09 (in/s^2)
The calculation uses SI units internally. The unit weight in pounds per inch converts to kilograms per meter by multiplying by 17.858.
Three plain strings on a 25.5 inch scale
E4 at 329.63 Hz with a 0.010 inch plain steel string (unit weight 0.000022274 lb/in) carries 16.30 lb. B3 at 246.94 Hz with a 0.013 inch string carries 15.46 lb, and G3 at 196.00 Hz with a 0.017 inch string carries 16.66 lb.
The three strings together pull with 48.4 lb, which is 21.97 kg or 215.4 N. A maker's chart unit weight of 0.00002216 lb/in for the 0.010 string gives 16.22 lb instead of 16.30, a difference of 0.5% caused by the steel density used.
How string tension arises
A stretched string vibrates at a pitch set by its length, its mass per length and its tension: the frequency is f = (1 / 2L) x sqrt(T / mu). Rearranged, T = mu (2 L f)^2. So for the same note and scale, a heavier string needs more tension, and a longer scale needs more tension for the same string and pitch. Players use tension figures to compare string sets or check what changes when moving to a different scale length or tuning.
Plain steel strings have a mass per length given by the area of the wire times the density of the steel, so only the gauge is needed. Wound strings combine a core with a wrap, and their weight depends on the makers' materials, so their unit weight should come from the chart that comes with the string.
Using the numbers wisely
The tension here is for a string at pitch, resting, with no bends. A set's total tension is useful for comparing sets, and instrument makers publish limits for their designs, which this page does not know. Treat it as a comparison tool and not as a guarantee that a set suits a given instrument.
Related tools: the note frequency converter for pitches, the BPM delay time calculator for studio timing, the key finder from notes and the chord identifier.
Assumptions and limits
- The string is ideal: uniform, perfectly flexible and vibrating at its fundamental pitch.
- Plain steel density defaults to 0.2836 lb per cubic inch, an example for string steel that you can edit.
- Wound strings need a unit weight from the maker; the page does not estimate it.
- Notes use equal temperament with the A4 reference you choose, 440 Hz by default as an example.
Frequently asked questions
Why does a longer scale length raise the tension?
For the same pitch and the same string, a longer vibrating length needs a higher tension. Tension grows with the square of the length when pitch and string are fixed, so a few millimeters of extra scale make a noticeable difference.
Where do I find the unit weight of a wound string?
String makers publish tables listing each string gauge and its unit weight, usually in pounds per inch. Use the value for the exact string and material you have, and select the unit weight option in the row.
Is the result the same as the charts from string makers?
It follows the same formula, so figures agree when the same unit weights, scale length and pitch are used. Small differences come from density values and from the constant for gravity used in the conversion.
Can I use this for bass, violin or ukulele strings?
Yes, as long as you know the note, the vibrating length and either the gauge of a plain steel string or the unit weight of the string. The physics is the same for any ideal string.