Hz to Cent Converter
This Hz to cent converter calculates the interval in cents between any two frequencies using cents = 1200 × log₂(f₂ / f₁). Auto-identifies the closest just or equal-tempered interval (5:4 major 3rd, 3:2 perfect 5th, etc.), shows frequency ratio, and includes A/B audio comparison.
Input — Two Frequencies
Result
Just vs Equal-Tempered Interval Reference
| Interval | 12-TET (¢) | Just (¢) | Just ratio | Difference (¢) |
|---|---|---|---|---|
| Unison | 0 | 0 | 1:1 | 0 |
| Minor 2nd (semitone) | 100 | 111.73 | 16:15 | +11.73 |
| Major 2nd | 200 | 203.91 | 9:8 | +3.91 |
| Minor 3rd | 300 | 315.64 | 6:5 | +15.64 |
| Major 3rd | 400 | 386.31 | 5:4 | −13.69 |
| Perfect 4th | 500 | 498.04 | 4:3 | −1.96 |
| Tritone | 600 | 590.22 / 609.78 | 45:32 / 64:45 | −9.78 / +9.78 |
| Perfect 5th | 700 | 701.96 | 3:2 | +1.96 |
| Minor 6th | 800 | 813.69 | 8:5 | +13.69 |
| Major 6th | 900 | 884.36 | 5:3 | −15.64 |
| Minor 7th | 1000 | 996.09 | 16:9 | −3.91 |
| Major 7th | 1100 | 1088.27 | 15:8 | −11.73 |
| Octave | 1200 | 1200 | 2:1 | 0 |
About Cents & Frequency Intervals
The cent is a logarithmic measure of musical interval: cents = 1200 × log₂(f₂ / f₁). There are exactly 1,200 cents per octave, 100 cents per equal-tempered semitone, and the cent applies the same way at any base frequency — going from 100 Hz to 100.58 Hz is the same "musical distance" (10 cents) as going from 1,000 Hz to 1,005.78 Hz. This makes it the standard unit for any frequency interval calculator that needs to be pitch-consistent across the entire audible range.
Why two-frequency intervals matter
Pure tuning intervals (just intonation) use simple integer ratios: 3:2 = perfect 5th, 5:4 = major 3rd, 6:5 = minor 3rd. These ratios produce maximally consonant sounds because the overtones align. Equal temperament (12-TET) tempers all intervals to a uniform semitone of exactly 100 cents — convenient for keyboards but slightly "wrong" compared to just intervals (a 12-TET major 3rd is 13.69 cents flat of the just 5:4 version).
Practical use cases
Choir directors use cents to analyse pitch drift across phrases. Studio engineers use it to tune samples and loops to a target — for example, shifting a sample by exactly 700 cents raises it a perfect 5th regardless of its original pitch. Microtonal composers use it to specify experimental scales (e.g., 24-TET quarter-tones, 19-TET, 31-TET, Bohlen-Pierce). Researchers use it to study cultural tuning traditions — gamelan (with its distinctive stretched octaves), maqam, and raga systems all use non-12-TET intervals best described in cents. Synthesizer engineers express oscillator detuning in cents — a chorus effect typically detunes one voice by ±5–20 cents to create beating.
Historical temperaments and meantone tuning
Before equal temperament became standard in the 18th–19th century, keyboard instruments used meantone temperament, well temperament, and Pythagorean tuning — each with different cent deviations per interval. For instance, quarter-comma meantone makes the major 3rd exactly pure (386.31 cents, matching just intonation) at the cost of a "wolf 5th" that can be as far as 737 cents from the ideal 702 cents. Entering historical tuning frequencies into this converter lets you measure these deviations precisely. You can also use the Hz to note converter to identify the nearest equal-tempered note for any historical pitch standard.
Interval names beyond an octave
For cents values above 1,200, this tool reduces them to a single-octave interval class plus the octave count. So 1,902 cents = "Just perfect 5th + 1 octave" (a "twelfth"). 2,400 cents = "Octave + 1 octave" = two-octave doubling. To hear any of these intervals directly, you can generate reference tones with the online tone generator — play f₁ in one browser tab and f₂ in another to compare.
How to convert Hz to cents: step-by-step worked example
To convert two frequencies to cents, apply the formula cents = 1200 x log2(f2 / f1) directly. Take A4 (440 Hz) as f1 and A5 (880 Hz) as f2: the ratio is 880 / 440 = 2.0, log2(2.0) = 1.0, and 1200 x 1.0 = 1200 cents exactly — one octave. Now try A4 (440 Hz) to E5 (659.26 Hz, the 12-TET perfect 5th): ratio = 659.26 / 440 = 1.4983, log2(1.4983) = 0.58333, x 1200 = 700 cents (the 12-TET perfect 5th). Contrast this with the just perfect 5th at a pure 3:2 ratio — 440 x 1.5 = 660 Hz gives 1200 x log2(1.5) = 701.96 cents, just 1.96 cents above the tempered version. Two handy reference values: a semitone is always 100 cents (e.g., 440 Hz to 466.16 Hz), and an octave is always 1200 cents (e.g., 261.63 Hz to 523.25 Hz) regardless of the starting pitch. For the inverse operation -- applying a known cents offset to a single reference frequency -- use the cent to Hz converter. To find the nearest note name for a single frequency, use the Hz to note converter.