Cents Calculator Music

Interval in cents —

Frequency ratio: —
Equal-tempered semitones: —
Direction: —
Nearest named interval: —
Cents off that interval: —

Cents measure the distance between two pitches on a logarithmic scale: 1200 times the base-2 logarithm of the frequency ratio. One equal-tempered semitone is 100 cents and an octave is 1200. For example, 440 Hz to 660 Hz is a 3:2 ratio, which gives 701.96 cents, a pure fifth sitting 1.96 cents above the tempered one.

About this tool

Tuners, instrument builders, microtonal composers and anyone checking an intonation problem need to know how far apart two pitches really are, and hertz alone do not say it: a 10 Hz gap is large in the bass and tiny at the top of a violin. Cents fix that by expressing every interval as a share of the octave. Enter a reference frequency and a second frequency and the page returns the interval in cents, the raw frequency ratio, the equivalent count of equal-tempered semitones, whether the second note is higher or lower, the nearest named interval and how many cents it strays from it. The working is listed line by line. One limit: the result describes pure sine-tone fundamentals; real instruments with stretched or inharmonic overtones, such as pianos and bells, can sound in tune at slightly different cent values.

How to use it

Enter the reference frequency
Type the starting pitch in hertz, such as 440 for concert A4 or 261.63 for middle C.
Enter the second frequency
Type the pitch you want to compare. A lower value gives a negative cent figure.
Read the interval
The cent value, ratio and semitone count update as you type, together with the nearest named interval.
Check the deviation
The cents-off figure shows how far the interval sits from equal temperament, which is the number to act on when tuning.

Examples

A 440 Hz to E 660 Hz

Reference frequency: 440
Second frequency: 660

Result Interval in cents: 701.96
Frequency ratio: 1.5
Equal-tempered semitones: 7.02
Direction: Up
Nearest named interval: Perfect fifth
Cents off that interval: 1.96

Ratio = 660 / 440 = 1.5
Cents = 1200 x log2(1.5) = 701.955
Semitones = 701.955 / 100 = 7.0196
Nearest equal-tempered step: 7 semitones (Perfect fifth), off by 1.96 cents

A pure 3:2 fifth is 701.96 cents, almost 2 cents wider than the fifth on a piano tuned in equal temperament.

880 Hz down to 440 Hz

Reference frequency: 880
Second frequency: 440

Result Interval in cents: -1,200
Frequency ratio: 0.5
Equal-tempered semitones: -12
Direction: Down
Nearest named interval: Octave
Cents off that interval: 0

Ratio = 440 / 880 = 0.5
Cents = 1200 x log2(0.5) = -1200
Semitones = -1200 / 100 = -12
Nearest equal-tempered step: -12 semitones (Octave), off by 0 cents

Halving the frequency is exactly one octave, shown as -1200 cents because the second note is lower.

The syntonic comma, 81:80

Reference frequency: 80
Second frequency: 81

Result Interval in cents: 21.51
Frequency ratio: 1.0125
Equal-tempered semitones: 0.22
Direction: Up
Nearest named interval: Unison
Cents off that interval: 21.51

Ratio = 81 / 80 = 1.0125
Cents = 1200 x log2(1.0125) = 21.5063
Semitones = 21.5063 / 100 = 0.2151
Nearest equal-tempered step: 0 semitones (Unison), off by 21.51 cents

The gap between a Pythagorean and a just major third is about 21.5 cents, small enough to round to a unison but clearly audible in sustained chords.

How it is calculated

c = 1200 × log2(f2 ÷ f1)

c: interval size in cents
f1: reference frequency in hertz
f2: second frequency in hertz

Alexander Ellis introduced cents in 1885 so that intervals could be added instead of multiplied. Because pitch perception is roughly logarithmic, the ratio f2 ÷ f1 is converted with a base-2 logarithm and scaled so that one octave (ratio 2) equals 1200 cents. Dividing by 100 gives equal-tempered semitones; rounding that to the nearest whole number names the interval, and the remainder in cents is the deviation from twelve-tone equal temperament.

When not to use it

Do not use it to name a chord; it compares exactly two pitches.
Avoid it for piano tuning targets, where stretched octaves deliberately depart from exact ratios.
It cannot read pitch from audio; you need the frequencies already measured.

Common mistakes

Entering the two frequencies in reverse order flips the sign of the answer, so a sharp note appears flat.
Reading a 10 Hz difference as the same interval at every register ignores that cents depend on the ratio.
Comparing against A4 = 440 Hz when the ensemble tunes to 442 Hz adds about 7.85 cents of error.
Treating a just interval as out of tune because it differs from the tempered value by a few cents.

Frequently asked questions

How many cents are in a semitone?

In twelve-tone equal temperament each semitone is exactly 100 cents, so twelve of them make the 1200-cent octave. Other tuning systems use semitones of different sizes: a Pythagorean diatonic semitone is about 90.2 cents and a just 16:15 semitone is about 111.7 cents.

How many cents can the ear detect?

Trained listeners comparing two steady tones one after the other can often hear differences of around 5 to 6 cents in the middle register, and less when the tones sound together and beat. For melodic playing, deviations under a few cents are usually inaudible to most audiences.

Why is a just fifth 701.96 cents instead of 700?

A just perfect fifth has a 3:2 frequency ratio, and 1200 × log2(1.5) is 701.955 cents. Equal temperament shrinks each fifth by almost 2 cents so that twelve fifths close exactly onto seven octaves, which is why a piano's fifths beat slightly.

What does a negative cent value mean?

It means the second frequency is lower than the reference. The size of the interval is the same as the positive value; only the direction changes. For example 880 Hz to 440 Hz is -1200 cents, one octave down.

How do I convert cents back to a frequency ratio?

Raise 2 to the power of cents divided by 1200. For 386.31 cents that gives 2^(0.32193) = 1.25, the 5:4 just major third. Multiply the reference frequency by that ratio to get the second pitch.

How large is the syntonic comma in cents?

The syntonic comma, the 81:80 gap between a Pythagorean major third and a just major third, is about 21.51 cents. The Pythagorean comma, the overshoot of twelve pure fifths over seven octaves, is about 23.46 cents.

Cite this tool

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APA

Tools Directory Editorial Team. (2026, October 12). Cents Calculator Music. Tools Directory. Retrieved October 27, 2026, from https://tools.milunir.com/video-audio/music-and-audio-theory/cents-calculator-music/

MLA

Tools Directory Editorial Team. “Cents Calculator Music.” Tools Directory, 12 Oct. 2026, https://tools.milunir.com/video-audio/music-and-audio-theory/cents-calculator-music/. Accessed 27 Oct. 2026.

Chicago

Tools Directory Editorial Team. “Cents Calculator Music.” Tools Directory. Last modified October 12, 2026. Accessed October 27, 2026. https://tools.milunir.com/video-audio/music-and-audio-theory/cents-calculator-music/.

Link

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