Music Interval Calculator
A musical interval is the distance between two pitches. In 12-tone equal temperament, the standard tuning of the piano and most Western music, every semitone multiplies frequency by the twelfth root of 2. This calculator takes a starting frequency and a number of semitones and returns the exact frequency ratio, the interval size in cents, and the frequency of the second note. Use it to check tunings, transpose pitches, understand how intervals map to frequency, or convert between semitones and cents for any interval from a unison to several octaves.
Music interval formula
Ratio = 2 ^ (semitones / 12)
Cents = 100 * semitones
Second frequency = starting frequency * ratio
Octaves = semitones / 12
Each equal-tempered semitone is the twelfth root of 2, so the ratio of an interval is 2 raised to the power of semitones divided by 12. One semitone is exactly 100 cents and one octave (12 semitones) is exactly 1,200 cents.
Common intervals in equal temperament
- Unison is 0 semitones, ratio 1.000, and 0 cents.
- A major third is 4 semitones, ratio about 1.260, and 400 cents.
- A perfect fifth is 7 semitones, ratio about 1.498, and 700 cents.
- An octave is 12 semitones, ratio exactly 2.000, and 1,200 cents.
- The international concert-pitch reference is A4 at 440 Hz under ISO 16.
Music intervals: frequently asked questions
How is a musical interval measured in semitones?
In 12-tone equal temperament, an octave is divided into 12 equal semitones. A minor second is 1 semitone, a major third is 4, a perfect fifth is 7, and an octave is 12. Each semitone is exactly 100 cents, so an octave is 1,200 cents.
What is the frequency ratio of a semitone?
In equal temperament, each semitone multiplies the frequency by the twelfth root of 2, which is approximately 1.059463. Raising this ratio to the power of the number of semitones gives the interval's overall frequency ratio. Twelve semitones gives exactly 2, a doubling, which is one octave.
How do cents relate to semitones?
A cent is one hundredth of an equal-tempered semitone, so 100 cents equals 1 semitone and 1,200 cents equals 1 octave. Cents are calculated as 1,200 times the base-2 logarithm of the frequency ratio. They give a fine-grained, logarithmic measure of pitch distance.
Why is equal temperament used here?
Equal temperament is the standard tuning for most Western instruments, including the piano, because it lets you play in any key with consistent interval sizes. Just intonation uses small whole-number ratios instead, but those differ by key, so equal temperament is the self-evident default for an interval calculator.
What reference frequency should I use?
The international standard concert pitch is A4 at 440 Hz, defined by ISO 16. You can enter any starting frequency you like; the calculator simply multiplies it by the interval ratio to find the second note's frequency.
Official sources
- International Organization for Standardization: ISO 16:1975 Acoustics, Standard tuning frequency.
- U.S. National Institute of Standards and Technology: SI units and physical quantities.
Reviewed by the CalculatorHub team, edited by James Graham, 16 June 2026. See our methodology.