๐ธ String Tension Calculator
The preset buttons are the frequencies for standard tuning (E2, A2, D3, G3, B3, E4).
Enter a string's linear mass density (mass per unit length), scale length, and target pitch frequency to calculate the tension on the string, derived from the physics of a vibrating string's fundamental frequency (f = v/2L, v = โ(T/ฮผ)). Handy as a reference when choosing guitar or bass strings.
How to use
- Enter the string's linear mass density (g/m). This is often listed in the string manufacturer's spec sheet as "unit weight".
- Enter the scale length (mm).
- Enter the target pitch frequency (Hz), or pick one of the preset buttons.
- The tension on the string is calculated automatically.
How the calculation works
From a stringโs linear density (mass per metre), the scale length (vibrating length) and the pitch (frequency), this tool calculates the tension on the string when tuned to that note. Tension T (N) = ฮผ ร (2 ร L ร f)ยฒ (ฮผ: linear density in kg/m, L: scale length in m, f: frequency in Hz) A stringโs fundamental frequency is f = โ(T/ฮผ) รท 2L, and this is that equation solved for tension. Results are shown in newtons (N), in pounds-force (lbf) as string makers usually quote, and in kilograms-force (kgf). The preset buttons select the notes of guitar standard tuning.
Worked example
Guitar 1st string (E4, 329.63 Hz), 0.40 g/m (about a .010 gauge), scale length 647.7 mm (25.5 in) T = 0.0004 ร (2 ร 0.6477 ร 329.63)ยฒ โ 72.9 N (about 16.4 lbf, 7.4 kgf) Tuning the same string down a semitone (Eโญ) multiplies the tension by about (1 รท 1.0595)ยฒ โ 0.89.
Things to be aware of
- Tension rises with the square of frequency: down a semitone is about 11% less, down a whole tone about 21% less, and down an octave a quarter.
- A longer scale length gives more tension with the same strings, so they feel stiffer.
- Makers often list โunit weightโ in lb/in; 1 lb/in is about 17,858 g/m.
FAQ
Where can I find the linear mass density (g/m)?
String manufacturers often publish this as โunit weightโ in their product specifications. If you donโt have it, you can approximate it from the stringโs material and diameter using cylinder volume ร material density.
Whatโs the formula?
A stringโs fundamental frequency follows f = v/(2L), where wave speed v = โ(T/ฮผ) (ฮผ is linear mass density, L is scale length, T is tension). Rearranging gives T = ฮผร(2Lf)ยฒ, which is what this tool calculates.
Does the result match the actual tension of real strings?
If the mass density, scale length, and frequency you enter are accurate, the theoretical tension should closely match reality. Real strings can differ slightly from published values due to core/winding construction and manufacturing variation.