About the Beat Frequency Calculator
This beat frequency calculator works out how fast the loudness of two nearly matching tones pulses. Enter two frequencies and it returns the beat frequency (their difference), the time between beats, the beats per minute, the pitch you actually hear (their average) and how far apart the tones are in cents. Switch modes to go the other way: enter a reference frequency and the number of beats you count, and it gives the two possible frequencies of the unknown tone.
It is useful for musicians tuning by ear against a reference fork or a neighbouring string, piano technicians setting temperament by counting beats, physics students studying wave superposition, and audio engineers chasing low-frequency wobble between detuned oscillators. The chart shows the beat envelope — the slow swell and fade of loudness — over two beat cycles.
Beats are clearly heard when the two tones are within roughly 10–15 Hz of each other; further apart they blur into roughness and then into two separate notes. The calculator assumes two steady pure tones of similar loudness.
With the default inputs, the beat frequency is 4 Hz. Change any value above to recalculate instantly.
How to use the beat frequency calculator
- 1Choose whether you know both tones or are finding an unknown tone.
- 2Enter the reference frequency in hertz.
- 3Enter the second frequency, or the number of beats you counted per second.
- 4Read the beat rate, beat period and the interval in cents.
- 5In unknown mode, use the two candidates and the tuning tip to identify the pitch.
Formula and method
When two sine waves of slightly different frequency are added, the trigonometric identity sin a + sin b = 2·sin((a + b)/2)·cos((a − b)/2) shows the result is a tone at the average frequency whose amplitude is modulated by a slow cosine at half the difference frequency. Loudness depends on the magnitude of that envelope, which peaks twice per cosine cycle, so the ear hears beats at the full difference |f₁ − f₂|.
If you know one frequency and count beats, the other tone is either f₁ + f_beat or f₁ − f_beat — counting alone cannot tell which. The interval in cents uses 100 cents per equal-tempered semitone, a convenient measure of how far out of tune two notes are.
- f₁, f₂
- Frequencies of the two tones (Hz)
- f_beat
- Beat frequency (Hz)
- T_beat
- Time between beats (s)
- f_heard
- Perceived pitch (Hz)
Worked examples
A440 against a tone at 444 Hz
The beat frequency is |440 − 444| = 4 Hz, so you hear four pulses per second (240 per minute) on a pitch of 442 Hz. The second tone is about 15.7 cents sharp.
Two slightly detuned middle C strings
The strings differ by 0.87 Hz, giving one slow beat every 1.15 s. That is only 5.7 cents apart — piano tuners hear such slow beats easily when tuning unisons.
Unknown string beating 3 times a second against A440
Three beats per second means the string is 3 Hz away from 440 Hz: either 437 Hz or 443 Hz. Tightening it slightly and listening whether the beats slow or quicken tells you which.
Frequently asked questions
What is beat frequency?+
Beat frequency is the rate at which the loudness of two overlapping tones of slightly different frequency rises and falls. It equals the difference between the two frequencies: 440 Hz and 444 Hz produce 4 beats per second.
How do musicians use beats to tune?+
Play the note together with a reference. If you hear beats, the two are out of tune; adjust until the beats slow down and disappear. Fewer beats per second means the pitches are closer together.
Why is the beat frequency not half the difference?+
The mathematical envelope oscillates at half the difference frequency, but loudness depends on the envelope’s magnitude, which peaks twice per cycle. So the audible beat rate is the full difference |f₁ − f₂|.
What is the largest beat frequency you can hear?+
Distinct beats are easy to hear up to roughly 10–15 Hz. Beyond that the pulsing becomes a rough, buzzy sound, and with larger differences the ear separates the sounds into two distinct notes.
Can beats tell me if a note is sharp or flat?+
Not by themselves: a beat rate only tells you how far apart the tones are. Raise the pitch a little — if the beats speed up, the note was already sharp; if they slow down, it was flat.