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What a cent is
A cent is a tiny unit for measuring pitch. There are 100 cents in one equal tempered semitone, and 1200 cents in one octave. Cents were invented so that musicians and instrument makers could talk about small tuning differences precisely. Saying a note is 15 cents sharp means something exact, while saying it is a little sharp means almost nothing.
Cents work on a logarithmic scale, which matches how hearing works. The ear hears pitch ratios, not frequency differences: the jump from 100 Hz to 200 Hz sounds the same size as the jump from 200 Hz to 400 Hz, because both are octaves, even though the second jump is twice as many hertz. Cents measure those ratios in equal steps, so 100 cents always sounds like the same distance, wherever you are in the range.
Cents, semitones and ratios
Converting between cents and semitones is simple division: divide cents by 100. So 50 cents is half a semitone, 200 cents is a whole tone, and 700 cents is a perfect fifth in equal temperament. Converting to a ratio uses the formula 2 to the power of cents divided by 1200. That formula gives the frequency ratio directly: 1200 cents gives 2, exactly one octave, and 100 cents gives about 1.05946, the semitone ratio.
Going the other way, from a ratio to cents, uses the logarithm: cents equal 1200 times log base 2 of the ratio. The famous just fifth, ratio 3/2, works out to about 701.96 cents, which is 1.96 cents sharper than the equal tempered fifth of 700 cents. The just major third, ratio 5/4, is about 386.31 cents, which is 13.69 cents flatter than the equal tempered third of 400 cents. Those small differences are audible to trained ears, and they are why choirs and string players sound different from pianos.
How to use the converter
Enter a value in cents, and the converter shows the semitone distance, the frequency ratio, and the closest simple just ratio with its error in cents. Enter a ratio as a numerator and denominator, and it shows the cents value. Try 700 cents first: the closest just ratio is 3/2, off by only 1.96 cents. Then try 400 cents: the closest just ratio is 5/4, off by 13.69 cents, which is the famous gap between just and equal tempered thirds.
Use the converter when tuning an instrument, when reading about historical temperaments, when working with microtonal music, or when a tuner reports a deviation and you want to know what it means in musical terms.
Why cents matter in practice
Cents are the working language of tuning. Piano tuners stretch octaves by a few cents to make the instrument sound in tune across its range. Guitarists check intonation by comparing the 12th fret harmonic with the fretted note, and the difference is measured in cents. Singers in choirs adjust by cents without thinking about it, drifting toward just intervals that sound beat free.
Cents also matter for instrument design. A fretless instrument or a voice can hit any pitch, so its player lives in cents. A fretted or keyboard instrument cannot, so its maker has to choose a temperament, a compromise about which intervals are pure and which are slightly off. Every temperament is a story told in cents.
Common mistakes
The most common mistake is treating cents as linear in hertz: 100 cents is not 100 Hz, and the same cents value means different hertz at different pitches. Another mistake is confusing cents with percent: a note 50 cents sharp is not 50 percent sharp, it is half a semitone sharp. Finally, remember that small cent values are real: 5 cents is audible to a good ear in a sustained chord, and 15 cents is audible to almost anyone.
Convert a few values now, especially the just ratios, and cents will stop feeling abstract. They are simply a ruler for pitch, marked in steps the ear can actually use.
Related calculators
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