Beat Frequency Calculator
The beat you hear when two tones close in pitch sound together — the beat frequency and the seconds between beats — with the tone you perceive, the gap in cents, and how many beats to count in ten seconds when tuning.
Two waves of nearly equal frequency drift in and out of step, so the sound swells and fades at a rate equal to the difference between them.
How the beat frequency calculator works
Two waves of nearly equal frequency drift in and out of step, so the sound swells and fades at a rate equal to the difference between them. What you hear is the average pitch, pulsing at the beat frequency. Tuners use it directly: count the beats against a reference, and the string is out by that many hertz. The gap in cents — hundredths of a semitone — says how far off that is musically.
Formula: f_beat = |f₁ − f₂|; perceived tone = (f₁ + f₂)/2; cents = 1200 log₂(f₁/f₂)
Worked examples
| Inputs | Beat frequency (Hz) | Note |
|---|---|---|
| A string 3 Hz sharp of A440 | 3 | three beats a second |
| Nearly in tune | 0.5 | a beat every two seconds |
| Too far apart | 40 | two separate notes |
FAQFrequently asked questions
What causes beats?
Two waves of nearly equal frequency alternately reinforce and cancel as they slip in and out of phase. The result is one tone at the average pitch, pulsing in loudness at the difference frequency.
How do I tune with beats?
Sound the string against a reference and adjust until the beats slow and stop. Each beat per second is one hertz of error; a piano tuner counts beats to set intervals precisely off pure.
What is a cent?
A hundredth of a semitone. Most people cannot hear a difference under about five cents; a 3 Hz error at A440 is nearly twelve.
When do beats stop being beats?
Above roughly 15 to 20 Hz the pulsing becomes a roughness and then two distinct tones. Below about 1 Hz the swell is slow enough to count individually.
Do beats work at any pitch?
Yes, but the same beat rate is a smaller error at high pitch: 3 Hz is 12 cents at A440 and only 3 cents at 1,760 Hz.
Where these figures come from
- NIST — CODATA 2018 fundamental physical constants — G, g₀, R, c
- NIST Special Publication 811 — Guide for the use of the International System of Units — unit conversions
- The Engineering ToolBox — material properties — specific heats, expansion coefficients, densities
- National Institute of Standards and Technology — the US measurement authority
Last checked: September 2026. Constants are the CODATA 2018 values; formulas are the standard textbook forms.