About BPM Math

BPM Math is a set of free tools for the arithmetic musicians and producers do constantly: what tempo a song is, how many milliseconds a dotted eighth is at 128 BPM, what reverb decay fits a bar, how long 64 bars runs, what frequency a note is, and what a progression becomes in a new key. Each one shows the formula and a table so you can check the number, or memorise it.

The formulas

Tempo is time arithmetic: a quarter-note beat at T BPM lasts 60,000 ÷ T milliseconds, and every other note value is a multiple of that (dotted × 1.5, triplet × 2⁄3). Pitch uses twelve-tone equal temperament with A4 at 440 Hz, so a note n semitones above A4 is 440 × 2^(n⁄12) Hz, and MIDI note numbers follow the same scale with A4 = 69. Intervals are measured in cents, 1,200 to the octave. Reverb pre-delay and decay by tempo follow the common producer rule of thumb (pre-delay around a 64th note, total reverb around a bar) and are marked as such: a starting point for the ear, not a law.

What this site doesn't do

It doesn't store what you enter, require an account, or analyse audio. The BPM counter times your taps; it does not listen to the song. Tempo-synced numbers are conventions that suit most mixes, and the right setting is whatever sounds right in yours.

Corrections

If a formula, convention or table here is wrong, email hello@bpmmath.com. The maths is stated on each page so a correction can be checked against it.