Equal Temperament Tuning Calculator
Twelve-tone equal temperament is the tuning system behind virtually every modern piano, guitar, and synthesiser. It divides each octave into twelve identical steps, so any note's frequency is the reference pitch multiplied by two raised to a fractional power. This calculator takes a reference frequency (such as A4 at 440 Hz) and how many semitones a target note sits above or below it, then returns the exact frequency, the interval size in cents, and the frequency ratio. Use it to retune to historical pitches, check a tuner, or understand the maths that lets every key sound consistent.
Equal temperament formula
Frequency = reference * 2^(semitones / 12)
Ratio = frequency / reference = 2^(semitones / 12)
Cents = 100 * semitones
Octaves = semitones / 12
Each semitone is the twelfth root of two, about 1.059463. Twelve semitones double the frequency, one octave. Negative semitone values produce notes below the reference.
Tuning context
- A4 at 440 Hz is the ISO standard concert pitch; baroque ensembles often use 415 Hz.
- An octave is 1,200 cents; an equal-tempered semitone is exactly 100 cents.
- Equal temperament makes all keys equivalent at the cost of slightly impure thirds and fifths.
- The equal-tempered fifth is about two cents narrower than a pure 3:2 fifth.
- Set the reference frequency to match your ensemble before transposing.
Equal temperament: frequently asked questions
What is equal temperament?
Twelve-tone equal temperament divides the octave into twelve equal steps, each a frequency ratio of the twelfth root of two, about 1.059463. This makes every key sound the same, which is why modern keyboards and fretted instruments use it. The trade-off is that intervals other than the octave are slightly out of tune compared with pure whole-number ratios.
How is a note frequency calculated?
Pick a reference pitch and its frequency, usually A4 at 440 Hz. The frequency of a note that is n semitones away is the reference frequency multiplied by two raised to the power of n divided by twelve. Twelve semitones up doubles the frequency (one octave); twelve down halves it.
Why is A4 set to 440 Hz?
A4 at 440 Hz is the international standard concert pitch, adopted as ISO 16. Many orchestras tune slightly higher, around 442 or 443 Hz, and historical or baroque ensembles often use 415 Hz. This calculator lets you set any reference frequency to match your ensemble.
What is a cent?
A cent is one hundredth of an equal-tempered semitone, so an octave spans 1,200 cents. Cents give a fine, logarithmic measure of pitch difference. A difference of a few cents is barely perceptible; differences above about ten cents are clearly audible to trained ears.
Does this work for instruments other than 12-tone?
This calculator assumes the standard twelve-tone equal-tempered octave. Microtonal systems divide the octave into different numbers of steps (for example 19 or 24), which use a different root. For standard Western tuning, twelve-tone equal temperament is correct.
Official sources
- UNSW School of Physics: Note names, MIDI numbers and frequencies.
- UNSW School of Physics: Music acoustics.
Reviewed by the CalculatorHub team, edited by James Graham, 17 June 2026. See our methodology.