String Tension Calculator
Estimate the tension of a vibrating string from its tuned pitch, scale length and linear density, in kilograms-force, newtons and pounds-force. Runs in your browser.
String tension
-
Show the math
A vibrating string's pitch depends on its tension, length and mass. Rearranged for tension:
T = μ × (2 × L × f)²
where μ is the linear density (kg/m), L the scale length (m) and f the frequency (Hz). Higher pitch, longer scale or a heavier string all raise the tension.
Everything is calculated in your browser.
What this does
A string tension calculator estimates the tension of a vibrating string from its tuned pitch, scale length, and linear density — in kilograms-force, newtons, and pounds-force.
How to use it
- Enter the tuned pitch.
- Enter the scale length.
- Enter the string’s linear density.
- Read the tension.
How it works
From the vibrating-string equation, where μ is linear density (kg/m), L the scale length (m), and f the frequency (Hz). Higher pitch, longer scale, or a heavier string all raise tension.
T = μ × (2 × L × f)²
Understanding your result
Tension is an estimate from pitch, scale length, and string gauge, and it is what determines how an instrument feels and stays in tune. Aim for a balanced tension across the set, a string far tighter or slacker than its neighbours feels uneven and can stress the neck. When changing gauge or tuning, check the total tension stays in the range the instrument is built for.
Example
A heavier gauge or a longer scale at the same pitch pulls noticeably tighter.
Sources & methodology
Last updated .
Frequently asked questions
How is string tension calculated?
From the vibrating string equation rearranged for tension: T = μ × (2 × L × f)², where μ is the linear density (kg/m), L the scale length (m) and f the frequency (Hz).
Where do I find a string’s linear density?
String makers publish a unit weight or mass per unit length for each gauge. Enter it in grams per metre; the tool converts internally.
What raises the tension?
A higher pitch, a longer scale length or a heavier (thicker) string all increase tension. Lowering any of them reduces it.
Do you store my numbers?
No. Everything is calculated locally in your browser.
Related tools
Note Frequency Calculator
Find the exact frequency of any musical note in any octave, with its MIDI number, wavelength and period. Retune the A4 reference to 432 Hz or any value. Runs in your browser.
Note to MIDI Converter
Convert between note names and MIDI numbers in both directions, with the frequency for each. Middle C is C4 (MIDI 60) and A4 is MIDI 69. Runs in your browser.
Cents & Interval Calculator
Measure the interval between two frequencies in cents and as a ratio, name the nearest equal-tempered interval, and convert cents back to a frequency ratio. Runs in your browser.
BPM to Delay Calculator
Turn any tempo into tempo-synced delay and reverb times, quarter, eighth, dotted and triplet note values in milliseconds, with their matching frequencies. Runs in your browser.