What is a cent in music?

A cent is one hundredth of an equal-tempered semitone, so there are 1200 cents in an octave. Cents give a fine-grained, perceptually even way to measure tuning differences that would be clumsy to express as raw hertz.

How do you convert a frequency ratio to cents?

The formula is cents = 1200 x log2(f2 / f1). A perfect octave (ratio 2) is exactly 1200 cents, a perfect fifth in just intonation (ratio 3/2) is about 702 cents, and an equal-tempered semitone is exactly 100 cents.

How many cents are in a semitone?

Exactly 100 cents in equal temperament. Twelve semitones of 100 cents each make up the 1200-cent octave, which is why a half-step shift equals 100 cents.

Why is an equal-tempered fifth not exactly 702 cents?

Equal temperament divides the octave into 12 identical steps, making the fifth exactly 700 cents. The pure just fifth (3/2 ratio) is about 702 cents, so the equal-tempered fifth is roughly 2 cents flat — a tiny, usually imperceptible compromise.

Can I use this for microtonal tuning?

Yes. Enter any two frequencies and the tool reports the exact cent interval, which is the standard unit for describing microtonal and non-Western tunings that fall between the usual 12 semitones.

Semitone & Cents Interval Calculator

Cents and semitones are the universal language of tuning. This tool measures the interval between any two pitches, reporting the frequency ratio, the number of equal-tempered semitones, and the precise value in cents, plus the nearest named interval.

How it works

Pitch perception is logarithmic: doubling the frequency always sounds like the same interval, an octave. So intervals are measured on a log scale. The octave is divided into 1200 cents, and the conversion from a frequency ratio is:

cents = 1200 x log2(f2 / f1)

Semitones are simply cents divided by 100, since there are 100 cents in each of the twelve equal-tempered semitones:

semitones = cents / 100 = 12 x log2(f2 / f1)

Worked example

For f1 = 440 Hz (concert A) and f2 = 660 Hz:

Ratio = 660 / 440 = 1.5
Cents = 1200 x log2(1.5) = 701.96 cents
Semitones = 7.02

That is a perfect fifth — 660 Hz is very close to the just-intonation fifth above A, just under the 700-cent equal-tempered fifth by about 2 cents.

Reference intervals

Interval	Equal-tempered cents	Semitones
Unison	0	0
Minor third	300	3
Major third	400	4
Perfect fifth	700	7
Octave	1200	12

Tips and notes

A negative cent value means the second frequency is lower than the first; the tool handles either order.
Use the cent figure directly when detuning an oscillator or planning a pitch-shift — most plugins accept cents as a parameter.
For just-intonation work, compare your measured cents against the pure ratios (fifth 701.96, major third 386.31) to see how far equal temperament strays. All calculations run locally in your browser.