What Is a String Tension Calculator?
A string tension calculator finds the tension in a vibrating string from its length, the frequency it produces, and its mass per unit length. This is fundamental in both physics and music — string tension determines pitch on guitars, pianos, and other instruments. Enter the string's properties and the calculator returns the tension, or rearranges to solve for frequency.
How to Use the Calculator
- Enter the string length — the vibrating length.
- Enter the frequency of the fundamental tone.
- Enter the mass per unit length (linear density).
- Calculate — see the string tension.
The String Tension Formula
For the fundamental frequency of a vibrating string:
T = 4 × L² × f² × μ
where T is tension, L is the vibrating length, f is the frequency, and μ is the mass per unit length. This comes from the wave equation for a string fixed at both ends.
How Each Factor Affects Pitch
| Change | Effect on Pitch |
|---|---|
| Higher tension | Higher pitch |
| Longer string | Lower pitch |
| Heavier string (more μ) | Lower pitch |
Why This Matters for Instruments
- Tuning: increasing tension raises pitch, which is how strings are tuned.
- String gauge: thicker strings have more mass per length and lower pitch at the same tension.
- Scale length: longer strings vibrate at lower frequencies.
- Playability: tension affects how a string feels under the fingers.
Frequently Asked Questions
How do you calculate string tension?
Use T = 4 L² f² μ, where L is the vibrating length, f is the frequency, and μ is the mass per unit length. The calculator applies this for you.
How does tension affect pitch?
Higher tension produces a higher pitch. This is why tightening a string raises its note and loosening it lowers the note.
Why do thicker strings sound lower?
Thicker strings have more mass per unit length, which lowers the frequency at the same tension and length, producing a lower pitch.
What is mass per unit length?
It is the linear density of the string — its mass divided by its length. Heavier, thicker strings have a larger value, affecting pitch and tension.
Is this string tension calculator free?
Yes — it is completely free, requires no signup, and solves for tension or frequency.