Harmonic Frequency Calculator

About this calculator

For a string fixed at both ends, the allowed standing-wave frequencies follow fₙ = n·v / (2L), where v is the wave speed on the string, L is the string's length, and n is the harmonic number (1, 2, 3...). The n=1 term is the fundamental frequency (the note you perceive as the pitch); n=2, 3, and beyond are overtones, and together this full harmonic series determines a string's characteristic timbre.

Instrument builders (luthiers) use this relationship when choosing string length, tension, and mass to hit target pitches on guitars, violins, and pianos, musicians use it to understand why fretting or stopping a string shortens it and raises its pitch, and physics students use it as the standard worked example of standing waves and resonance on a bounded medium. Enter the harmonic number, wave speed, and string length to find the frequency.