Cents Interval Calculator
The cent is the standard fine-grained unit for measuring musical intervals. One octave is divided into 1,200 cents, and one equal-tempered semitone is 100 cents. This makes cents ideal for comparing tuning systems, measuring how far an instrument is out of tune, or describing micro-intervals that fall between the notes of the piano. Enter any two frequencies in hertz and this calculator returns the interval between them in cents, along with the raw frequency ratio and the equivalent number of equal-tempered semitones.
Cents interval formula
cents = 1200 * log2(f2 / f1)
ratio = f2 / f1
semitones = cents / 100
octaves = cents / 1200
log2(x) is the base-2 logarithm, computed as ln(x) / ln(2). A 2:1 ratio (octave) gives exactly 1,200 cents. A descending interval (f2 below f1) gives a negative cents value.
How cents are used
- An octave is 1,200 cents; an equal-tempered semitone is exactly 100 cents.
- The just perfect fifth (3:2) is 701.96 cents; the equal-tempered fifth is 700 cents.
- The just major third (5:4) is 386.31 cents; the equal-tempered major third is 400 cents.
- Differences smaller than about 5 to 6 cents are at the threshold of human pitch discrimination for sustained tones.
- Tuners and microtonal composers routinely specify pitch to a fraction of a cent.
Cents intervals: frequently asked questions
What is a cent in music?
A cent is a logarithmic unit of musical interval equal to one hundredth of an equal-tempered semitone. An octave (a 2:1 frequency ratio) spans exactly 1,200 cents, and a 12-tone equal-tempered semitone spans exactly 100 cents. The unit was introduced by Alexander Ellis in the 19th century as a precise way to compare intervals across tuning systems.
What is the formula for cents between two frequencies?
Cents = 1200 * log2(f2 / f1), where f1 is the lower (or reference) frequency and f2 is the upper frequency. Because the base-2 logarithm of a 2:1 ratio is 1, multiplying by 1,200 yields exactly 1,200 cents for an octave. The result is positive when f2 is higher than f1 and negative when it is lower.
How many cents is a just perfect fifth?
A just (Pythagorean) perfect fifth has a frequency ratio of 3:2, which equals 1200 * log2(1.5) = 701.96 cents. The equal-tempered perfect fifth is exactly 700 cents, so the just fifth is about 1.96 cents wider. This small difference is why equal temperament sounds slightly different from pure just intonation.
Can the result be negative?
Yes. If the second frequency is lower than the first, the interval is descending and the cents value is negative. For example, going from 440 Hz down to 220 Hz is an octave down, which is minus 1,200 cents.
Sources and definitions
- The cent is defined as 1/1200 of an octave: cents = 1200 * log2(f2/f1). This is a standard mathematical definition of the unit.
- National Institute of Standards and Technology: SI units reference (frequency in hertz).
Reviewed by the CalculatorHub team, edited by James Graham, 19 June 2026. See our methodology.