Cents Interval Calculator

Cents equal 1200 times the base-two logarithm of the frequency ratio, written 1200 x log2(f2 / f1). Because an octave doubles frequency, log2(2) is 1 and the octave works out to exactly 1200 cents.

There are 100 cents in an equal temperament semitone, so twelve semitones fill the 1200 cent octave. The calculator divides the cents value by 100 and shows that semitone count next to the result.

Enter both values in hertz. Decimals are fine, for example 466.16 Hz. The interval, semitones and ratio are displayed rounded to two or four places, which is why a nominal 100 cent semitone reads as 99.99.

A negative value means Frequency 2 is lower than Frequency 1, so the interval points downward. Its size is the same as the upward interval, only the sign flips. For example 880 Hz to 440 Hz gives minus 1200 cents.

A gap measured in hertz sounds much wider at low pitches than at high ones, because pitch is logarithmic. Cents describe the perceived interval size no matter where it sits on the keyboard, so intonation comparisons stay fair.

It is simply Frequency 2 divided by Frequency 1. A ratio of 2 is an octave, 1.5 is a just perfect fifth, and about 1.3333 is a just perfect fourth. Ratios are how tuning systems like just intonation are defined.

700 cents is the equal temperament fifth, tuned so twelve fifths close the circle. The pure 3 to 2 ratio of a just fifth is slightly wider, about 701.96 cents, and that roughly two cent gap is the compromise behind equal temperament.

A cent is one hundredth of a semitone and sits near the limit of what a trained ear can detect on sustained tones. Tuners commonly aim within a few cents of the target, and beats between two notes fade as the interval nears its pure ratio.

Yes. The calculation runs entirely in your browser using the log2 formula, so the frequencies you type never leave your device and nothing is uploaded to a server.