Why a tempo is really a duration
Beats per minute is a rate, and every rate has a reciprocal. Sixty seconds contain 60,000 milliseconds, so a tempo of 120 beats per minute means each beat occupies 60,000 ÷ 120 = 500 milliseconds. That single division is the whole idea; everything else on this page is bookkeeping about which note value you mean and whether it carries a dot or a triplet bracket.
The conversion matters in two places. In a music classroom it makes rhythm concrete: a student who cannot feel the difference between an eighth-note triplet and a sixteenth note can see that at 120 BPM one lasts 166.67 milliseconds and the other 125, and that the 41.67 ms between them is a twelfth of a beat rather than an abstraction. In a studio it is a practical necessity, because a delay pedal, a hardware LFO or a plug-in without host sync asks for milliseconds or hertz, not for note values.
The same arithmetic underlies how sequencers store tempo. A Standard MIDI File does not record beats per minute at all — the Set Tempo meta event records microseconds per quarter note, which is this calculation already performed. The default value of 500,000 microseconds is exactly the 500 millisecond quarter note of 120 BPM, which is why 120 is the tempo an empty session so often opens at.
Reading the formula piece by piece
Start with the beat. One beat lasts 60,000 ÷ BPM milliseconds, and that is true whatever note value the beat happens to be — the metronome defines the beat, not the notation.
Next, express the note you want as a number of beats. If the tempo counts quarter notes and you want an eighth, the eighth is half a beat, so you multiply by 4 ÷ 8 = 0.5. In general the factor is the beat unit divided by the note value: a whole note against a quarter-note beat is 4 ÷ 1 = 4 beats, a sixteenth is 4 ÷ 16 = 0.25 beats. Setting the beat unit to something other than 4 handles time signatures such as 6/8 or 2/2, where the tempo marking counts eighths or halves.
Finally apply the modifier. A dot adds half the note's own value, so a dotted note is 1.5 times the straight one — a dotted quarter is a quarter plus an eighth. A triplet fits three notes into the space of two, so each is 2/3 of the straight value. Those two factors are exact ratios, not approximations, and they compose with everything before them by simple multiplication.
Two further quantities fall out at no extra cost. The frequency is the reciprocal in seconds: a note of 250 milliseconds repeats four times a second, which is 4 Hz, and that is the number an LFO rate control wants. The sample count is the duration in seconds times the sample rate: 250 milliseconds at 48 kHz is 12,000 samples, which is what you need when you are nudging a region by an exact subdivision or writing a buffer length in code.
Worked example: a dotted-eighth delay at 90 BPM
You are working on a track at 90 BPM in 4/4 and want the classic dotted-eighth delay — the pattern that pushes against a straight eighth-note part and makes it sound like a cross-rhythm. The session runs at 44.1 kHz.
- One beat. 60,000 ÷ 90 = 666.667 ms per quarter note.
- The eighth note in beats. The beat unit is 4 and the note value is 8, so 4 ÷ 8 = 0.5 beats.
- Apply the dot. 0.5 × 1.5 = 0.75 beats.
- Duration. 0.75 × 666.667 = 500.00 ms. Set the delay to 500 milliseconds.
- Frequency. 1000 ÷ 500 = 2 Hz, so an LFO at 2 Hz cycles once per dotted eighth.
- Samples. 0.5 s × 44,100 = 22,050 samples exactly.
- The bar. Four beats at 666.667 ms is 2,666.67 ms, so 2,666.67 ÷ 500 = 5.333 dotted eighths fit in a bar.
That last line is the musical point. Because a dotted eighth is three sixteenths and a bar of 4/4 is sixteen sixteenths, the pattern does not divide evenly into the bar: it takes three bars for the repeats to line up with the downbeat again. The rhythm that produces is the reason the setting is used, and it is visible in the arithmetic before you hear a note.
Compare it with a straight eighth at the same tempo, 333.33 ms, or a quarter-note triplet, 666.667 × 2/3 = 444.44 ms. All three are easy to confuse by ear and impossible to confuse on the clock.
Choosing a subdivision and reading the result
Pick the subdivision by what you want the repeat to do against the part it sits on. A quarter-note delay reinforces the pulse and thickens it. An eighth-note delay doubles the density. A dotted eighth cuts across a straight eighth pattern and reads as syncopation. A triplet against duple material produces the same tension in the other direction. The milliseconds are just the way to tell the equipment which of those you meant.
Read the frequency output when you are setting anything that oscillates rather than repeats — tremolo depth cycles, filter sweeps, auto-pan. Read the sample count when you are working below the level of the note: writing a plug-in, setting a buffer, or aligning two takes by an exact number of samples. Read the bar duration when you are laying out a structure and want to know whether an eight-bar intro is fifteen seconds or twenty-two.
One caution about tempo values. Many round tempi produce recurring decimals — 60,000 ÷ 140 is 428.5714… milliseconds, and no dial setting is exactly right. This is harmless for a delay, where a fraction of a millisecond is inaudible, and it matters for a rendered loop, where 1,000 repetitions of a rounding error is an audible drift. Where accuracy matters, let the host sync the effect to the transport rather than typing a rounded number in.
If you are working in the opposite direction — from a heard duration to a tempo — invert the same expression: BPM = 60,000 ÷ (milliseconds per beat). A tapped 480 ms beat is 125 BPM.
Note durations at 120 BPM with a quarter-note beat
| Note | Straight (ms) | Dotted (ms) | Triplet (ms) | Straight (Hz) |
|---|---|---|---|---|
| Whole | 2,000.00 | 3,000.00 | 1,333.33 | 0.50 |
| Half | 1,000.00 | 1,500.00 | 666.67 | 1.00 |
| Quarter | 500.00 | 750.00 | 333.33 | 2.00 |
| Eighth | 250.00 | 375.00 | 166.67 | 4.00 |
| Sixteenth | 125.00 | 187.50 | 83.33 | 8.00 |
| Thirty-second | 62.50 | 93.75 | 41.67 | 16.00 |
Generated from t = (60000 / 120) × (4 / v) × m. The calculator rebuilds this table for whatever tempo and beat unit you enter.
One beat in milliseconds at common tempi
| Tempo (BPM) | Quarter note (ms) | Eighth note (ms) | Bar of 4/4 (ms) |
|---|---|---|---|
| 60 | 1,000.00 | 500.00 | 4,000.00 |
| 80 | 750.00 | 375.00 | 3,000.00 |
| 90 | 666.67 | 333.33 | 2,666.67 |
| 100 | 600.00 | 300.00 | 2,400.00 |
| 120 | 500.00 | 250.00 | 2,000.00 |
| 128 | 468.75 | 234.38 | 1,875.00 |
| 140 | 428.57 | 214.29 | 1,714.29 |
| 160 | 375.00 | 187.50 | 1,500.00 |
| 174 | 344.83 | 172.41 | 1,379.31 |
Only tempi that divide 60,000 exactly give whole-millisecond beats; 120, 100, 80 and 60 do, while 140 and 174 do not.
Compound metres count differently
In 6/8, 9/8 and 12/8 the tempo marking usually counts eighth notes, but the pulse a listener feels is the dotted quarter — three eighths grouped together. Set the beat unit to the eighth note so the tempo is interpreted correctly, then select the quarter note with the dotted modifier to get the felt pulse in milliseconds. At 180 eighths per minute an eighth is 333.33 ms and the dotted-quarter pulse is 1,000 ms, which is a comfortable 60 pulses a minute even though the tempo marking reads 180.
Assumptions and limits
- Constant tempo. Every figure assumes the tempo holds. Across a ritardando or a tempo map, each section needs its own conversion.
- Notated values, not performed ones. Swing, rubato and human timing all move notes off the grid deliberately. A swung eighth pair is not two equal 250 ms notes at 120 BPM, and no note-value arithmetic captures that.
- Delay time is not delay character. This gives the interval between repeats. Feedback, filtering, modulation and whether the delay is analogue-modelled or clean are separate decisions that do not change the timing.
- Latency is not included. Converters, plug-ins and monitoring paths add their own delay. If you are matching a hardware unit by ear, measure the round-trip latency separately.
- Sample counts round. Only durations that land on a whole number of samples are exactly representable; hosts keep fractional positions internally and round at placement, so error does not accumulate across repeats.
- Tempo can be written several ways. A metronome marking, a MIDI Set Tempo value in microseconds per quarter note, and a milliseconds-per-beat figure are three notations for one quantity.
Key terms
- Beat unit
- The note value the tempo counts, written as the lower number of the time signature. A tempo of 100 means something different in 4/4 than in 2/2, because the beat is a different length of note.
- Dotted note
- A note followed by a dot, lasting one and a half times its undotted value. The dot adds half the note's own duration, so a dotted quarter equals a quarter plus an eighth.
- Triplet
- Three notes played in the time normally occupied by two of the same value, so each lasts two-thirds as long. Three eighth-note triplets fill one quarter-note beat.
- Set Tempo
- The Standard MIDI File meta event that stores tempo as microseconds per quarter note. Its default of 500,000 corresponds to 120 BPM.
Related conversions in music and audio
Duration is one of two axes that a musical calculation runs along; pitch is the other, and it works by ratios rather than reciprocals. Where a note length is a linear function of the beat, a pitch is an exponential function of a semitone count — twelve equal steps to a doubling of frequency. The note frequency calculator turns a note name into hertz from the A4 = 440 Hz reference, and the cents pitch difference calculator measures how far apart two frequencies are on that logarithmic scale. If you need the same music written for a differently pitched instrument, the music transposition calculator handles the interval bookkeeping.
The one place the two axes meet is in tape and sample-rate manipulation. Play a recording back at a different speed and duration and pitch move together in exact inverse proportion: halve the playback rate and every note lasts twice as long while every frequency drops an octave. Modern time-stretching and pitch-shifting exist precisely to break that link, letting you change one without the other.
Outside music, the same reciprocal thinking turns any rate into a duration. Words per minute converts to seconds per word the same way beats per minute converts to milliseconds per beat, which is what the speech time calculator does for a script. Rate and duration are the same fact in two costumes, and the division that separates them is always 60,000 over the rate.