A vibrating string obeys Mersenne’s law: its frequency is f = (1 ÷ 2L) × √(T ÷ μ), where L is the vibrating length, T the tension and μ the mass per unit length (unit weight). Turned around, the tension needed to reach a pitch is T = μ × (2Lf)². Tension grows with the square of both the scale length and the frequency – tuning a string up a whole tone raises its tension by about 26%, and a 25.5″ guitar needs about 6% more tension than a 24.75″ one for the same strings.
The unit weight depends on gauge, material and construction (plain steel, round, half-round or flat wound, nylon, bronze or nickel wrap), so it is best taken from the manufacturer’s tables. This calculator embeds D’Addario’s published unit weights for twelve string families: plain steel, XL nickel-plated round wound, stainless round, half-round and flat wound, phosphor bronze (round and polished), 80/20 and 85/15 brass, clear nylon, silver-plated wound nylon and electric bass nickel round wound. Gauges not in the table are interpolated.
Use it to design a balanced set, check what happens in drop or baritone tunings, or choose gauges for a different scale length.
How to use the Guitar String Tension Calculator
- Scale length
- Pitch
- Note
- Octave — Standard guitar tuning: E2 A2 D3 G3 B3 E4; bass: E1 A1 D2 G2.
- Frequency
- Calculate
- String type
- String gauge (diameter) — e.g. 0.010 for a “10” high E, 0.046 for a low E in a 10–46 set.
- Unit weight
- Target tension
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How it works
The note and octave give the frequency with A4 = 440 Hz (or enter any frequency). The tool looks up the unit weight for the string type and gauge in D’Addario’s table (lb/in), converts it to kg/m and computes T = μ(2Lf)². In target mode it solves μ = T ÷ (2Lf)² and lists the nearest D’Addario gauges.
Worked example
A D’Addario .010 plain steel string (PL010, unit weight 2.215 × 10⁻⁵ lb/in = 3.9555 × 10⁻⁴ kg/m) tuned to E4 = 329.63 Hz on a 25.5″ (0.6477 m) scale: 2 × 0.6477 × 329.63 = 427.0 m/s, squared 182,330, times 3.9555 × 10⁻⁴ = 72.1 N = 16.2 lb (7.35 kg). Tuned down to E♭4 (311.13 Hz) the same string carries 14.5 lb.
Selected D’Addario unit weights
| String type | Gauges (in) | Unit weight (lb/in) |
|---|---|---|
| Plain steel (PL) | .009 / .010 / .011 / .012 | 1.794 / 2.215 / 2.680 / 3.190 × 10⁻⁵ |
| Nickel-plated steel round wound (NW) | .024 / .032 / .042 / .046 | 1.0857 / 1.9347 / 3.2279 / 3.8216 × 10⁻⁴ |
| Phosphor bronze round wound (PB) | .022 / .030 / .042 / .053 | 0.9876 / 1.7851 / 3.4471 / 5.3270 × 10⁻⁴ |
| Clear nylon (NYL) | .028 / .032 / .041 | 2.216 / 2.894 / 4.751 × 10⁻⁵ |
| Bass nickel round wound (XLB) | .045 / .065 / .080 / .100 | 3.724 / 7.957 / 11.602 / 17.969 × 10⁻⁴ |
Formula
T = μ × (2 × L × f)² (μ in kg/m, L in m, f in Hz → T in N)
T (lb) = UW (lb/in) × (2 × L (in) × f)² ÷ 386.09
f of a note = 440 × 2^((MIDI − 69) ÷ 12)
Worked example
Inputs — Scale length: 25.5 in; Pitch: Choose a note; Note: E; Octave: 4; Calculate: Tension from string type and gauge; String type: Plain steel (PL); String gauge (diameter): 0.01 in.
Results — String tension = 72.12; Unit weight used = 0.00039555; Frequency = 329.628 Hz; Nearest note = E4; Unit-weight source = D’Addario plain steel .010″ (PL) – published unit weight 2.2150e-5 lb/in; How it feels = Typical for guitar (14–20 lb).
Key terms
- Unit weight (μ)
- Mass per unit length of the string, e.g. lb/in or kg/m.
- Gauge
- String diameter, in thousandths of an inch (a “10” is 0.010″).
- Scale length
- Vibrating length from nut to saddle.
- Mersenne's law
- f = (1/2L)·√(T/μ) – the frequency of an ideal vibrating string.
- Round / half-round / flat wound
- Wrap wire profiles; flat wound strings are smooth and slightly heavier.
Frequently asked questions
How much tension is on a guitar string?
Most guitar strings in standard tuning carry 13–20 lb (58–90 N); a full 10–46 set adds up to roughly 100 lb (about 45 kg).
What is the tension of a .010 high E on a 25.5″ scale?
With D'Addario's unit weight of 0.00002215 lb/in at E4 (329.63 Hz): 0.00002215 × (2 × 25.5 × 329.63)² ÷ 386.09 ≈ 16.2 lb.
Does a shorter scale length reduce tension?
Yes, with the square of the length: the same .010 on a 24.75″ scale carries 15.3 lb instead of 16.2 lb.
How much does down-tuning lower the tension?
Each semitone down cuts tension by about 11%; a whole step (two semitones) by about 21%.
What is a balanced-tension set?
A set whose gauges are chosen so every string has a similar tension, giving a more even feel under the fingers.
How do I measure string tension?
Directly only with a tension meter; normally it is calculated from unit weight, scale length and pitch as here.
Why do wound strings of the same gauge have different tensions?
The core-to-wrap ratio and the wrap material (nickel, bronze, brass, stainless) change the mass per inch, so the unit weight differs.