Cents and Pitch Interval Calculator

1. Enter the first, reference frequency in hertz.
2. Enter the second frequency to compare.
3. Read the interval in cents, the standard fine unit of pitch.
4. See the same interval in semitones, as a ratio and in octaves.

A positive value means the second frequency is higher; a negative value means it is lower.

A cent is the standard fine unit for measuring musical intervals. There are 1200 cents in an octave and 100 cents in an equal-tempered semitone, so a cent is a hundredth of a semitone, far smaller than most people can hear on its own.

Cents let musicians and tuners describe tiny differences in pitch precisely. Saying a note is 15 cents sharp is far clearer than trying to express the same thing as a fraction of a hertz. Because a cent is the same size relative to pitch anywhere on the scale, it gives tuners, instrument makers and software a single shared language for describing how close two notes really are, from the deepest bass to the highest treble.

1. Divide the second frequency by the first to get their ratio.
2. Take the base-two logarithm of that ratio.
3. Multiply by 1200, the number of cents in an octave.
4. Divide by 100 for the interval in semitones.

Because the scale is logarithmic, the same interval gives the same number of cents no matter where it sits on the frequency range, which is exactly how our ears perceive pitch rather than raw frequency gaps.

Compare 440 hertz, concert A, with 466.16 hertz, the A sharp above it. The ratio is about 1.0595, and 1200 times the base-two log of that is almost exactly 100 cents, one semitone. Now compare 440 with 445: the interval is about 19.6 cents, meaning the second note is roughly a fifth of a semitone sharp, enough to sound noticeably out of tune. That gap of just five hertz barely looks like anything written down, yet in cents it is immediately obvious as a tuning error a careful listener would flag straight away.

The Frequency Ratio

Cents depend only on the ratio of the two frequencies, not their absolute values, so 100 to 200 Hz is the same octave as 400 to 800.

Direction

If the second frequency is lower than the first, the interval is negative, showing a drop in pitch.

Tuning System

Equal temperament puts semitones at exactly 100 cents, while just intonation places some intervals a few cents away.

Reference Choice

Swapping which frequency is first flips the sign but keeps the size of the interval the same.

Common intervals have well-known cent values in equal temperament.

A just perfect fifth is about 702 cents, two cents wider than the equal-tempered fifth, a difference trained ears can notice, and it is one reason some players prefer the sound of just intonation.

Checking Tuning

Measure how far a note is from its target pitch, in the same units a tuner uses.

Comparing Temperaments

See how just or historical tunings differ from equal temperament, interval by interval.

Sound Design

Set precise detune amounts on oscillators, where cents are the standard control.

1. Using Hertz Differences

A fixed hertz gap is a bigger interval at low pitches than high ones; cents fix this by using ratios.

2. Ignoring the Sign

A negative result simply means the second note is lower, not that anything is wrong.

3. Confusing Cents and Semitones

There are 100 cents in a semitone, so do not read 100 cents as 100 semitones.

4. Expecting Just and Equal to Match

Just intervals sit a few cents from equal-tempered ones, so small differences are expected.

The cents formula is exact for any two frequencies, so the interval is precise. It measures pitch distance, not which notes are named.

Cents equal 1200 times the base-two logarithm of the higher frequency divided by the lower. From 440 to 466.16 Hz is 100 cents.

There are 100 cents in an equal-tempered semitone, and 1200 cents in a full octave.

A cent is a hundredth of a semitone, the standard fine unit for describing small differences in pitch and tuning.

Trained listeners can often notice differences of about 5 to 10 cents, while a difference under 3 cents is very hard to detect.

A fixed hertz gap is a larger interval at low pitches than high ones. Cents use the ratio, so the same interval is the same value anywhere.

An equal-tempered perfect fifth is 700 cents. A pure, just fifth is about 702 cents, two cents wider.

Yes. If the second frequency is lower than the first, the interval is negative, showing a drop in pitch.

Enter your base frequency and the detuned one to see the cents between them, or work backwards from the cents you want.

No. The calculator runs entirely in your browser and nothing you enter is stored or sent anywhere.

• Cent (music) (Wikipedia).
• Musical interval (Wikipedia).
• Just intonation (Wikipedia).