String Tension Calculator (Guitar and Plain Strings)
Tension of a plain string tuned to a given note on a given scale length, in newtons, kilograms-force and pounds, with how it changes around the note.
Results
The dashed line marks the value you entered.
What this tool does
A string's pitch is set by its length, its tension and its mass per metre, as Mersenne worked out in the 17th century: f = √(T/μ) ÷ 2L. Turned round, it tells you how hard a string pulls on the neck once tuned — a plain steel .010 high E on a 25.5-inch scale comes to about 7.4 kgf (16 lbf), close to what string makers publish. Tension rises with the square of the frequency, so tuning up a semitone adds about 12 %. The formula is exact only for plain strings; for wound strings use the maker's unit weight instead of a diameter.
Formula
T = μ (2 L f)² · μ = ρ π d² ÷ 4 (Mersenne: f = (1 ÷ 2L) √(T ÷ μ))
Variables
| Symbol | Meaning | Unit |
|---|---|---|
l | Scale length (nut to saddle) | mm |
f | Frequency | Hz |
dm | String diameter | mm |
ro | Density | kg/m³ |
T | String tension | N |
TK | Tension in kilograms-force | kgf |
TL | Tension in pounds-force | lbf |
MU | Mass per metre | g/m |
WS | Wave speed | m/s |
TS | Tension one semitone higher | N |
Worked example
- Scale length (nut to saddle)648 mm
- Frequency329.63 Hz
- String diameter0.254 mm
- Density7850 kg/m³
- String tension72.6 N
- Tension in kilograms-force7.40 kgf
- Tension in pounds-force16.32 lbf
- Mass per metre0.3978 g/m
- Wave speed427.2 m/s
- Tension one semitone higher81.5 N
Limitations
- The default values are typical reference figures, not measurements of your situation. Replace them with your own data whenever you have it.
- Mixing units is the most common source of error. Convert every input to the units shown next to each field before calculating.