Music · Strings
Guitar string tension calculator.
Enter the scale length, the note a string is tuned to and its gauge (or the unit weight from the maker’s chart) to estimate how hard that string pulls.
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Estimated tension
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How do you calculate string tension?
A stretched string vibrates at f = (1 / 2L) × √(T / μ), where L is the vibrating length, T the tension and μ the mass per unit length. Solve for tension: T = μ × (2 L f)². Mersenne’s laws follow from the same relation: a string at four times the tension sounds an octave higher.
Worked example. A .010 plain steel high E string (E4, 329.63 Hz) on a 25.5 in scale. Steel at 7,850 kg/m³ gives μ = 0.3978 g/m. T = μ × (2 × 0.6477 m × 329.63 Hz)² = 72.5 N, or 16.3 lb.
Scale length matters. For the same string and pitch, tension scales with the square of the scale length. The same .010 string on a 24.75 in scale comes out at 15.4 lb, about 5.8% lower.
Limits. The plain-string mode treats the string as solid steel; the density of steel usually ranges between 7,750 and 8,050 kg/m³, and 7,850 is used here. Wound strings are heavier than their core diameter suggests, so enter the unit weight published by the string maker. The result is an ideal-string estimate and ignores stiffness. Do not tune a string above the pitch its maker rates it for: it can break or strain the neck and bridge.
Frequently asked questions
What is the string tension formula?
T = mu x (2 x L x f)^2, with tension in newtons, mu in kg per metre, L in metres and f in hertz. Divide newtons by 4.448 for pounds-force.
How many pounds of tension is a .010 high E string?
About 16.3 lb on a 25.5 in scale tuned to E4, using solid steel at 7,850 kg/m3. Makers’ published figures can differ slightly.
Why do wound strings need unit weight?
A wound string is a core wrapped in wire, so its mass per length is not that of a solid steel rod of the same outer diameter. The maker’s published unit weight accounts for it.
What happens to tension if I tune up a semitone?
Frequency rises by about 5.9%, so tension rises by about 12.2% (the frequency ratio squared, 1.059463 x 1.059463).
Does a longer scale length mean more tension?
Yes. For the same string and pitch, tension grows with the square of the scale length, which is why longer-scale guitars feel stiffer.
Sources
Opened
- Wikipedia: String vibration
- Wikipedia: Mersenne's laws
- Wikipedia: Steel (density 7,750 to 8,050 kg/m3)
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Not professional advice
Estimates for planning only, not engineering or luthier advice. Real string tension depends on construction, and manufacturers publish their own figures. Check the string maker’s rated tension and your instrument’s limits before tuning up or changing gauges.