BPM calculator
At 120 beats per minute a quarter note is exactly 500 milliseconds and a bar of four is exactly two seconds. Every other tempo is easiest to reason about relative to it — 60 BPM doubles everything, 240 halves it. It is also why so much dance music sits between 120 and 130: the arithmetic is clean and the tempo sits close to a brisk walking pace.
A beat lasts 60,000 divided by the tempo in milliseconds. At 120 BPM a quarter note is 500 ms, an eighth 250 ms, a dotted quarter 750 ms and a quarter triplet 333 ms. A bar of four takes two seconds.
How to work out delay times
Tempo-synced delay is the difference between an effect that sits in a track and one that fights it. A delay set to an arbitrary 380 ms against a 120 BPM song produces repeats that drift across the beat and muddy everything; the same delay at 375 ms locks to a dotted eighth and reads as part of the arrangement. Most plugins now offer host sync and do this for you, which is exactly when knowing the underlying numbers stops being necessary and starts being useful — for hardware, for guitar pedals, and for understanding why a preset does not fit.
Questions
Divide 60,000 by the tempo. At 120 BPM that is 500 ms per quarter note.