Semitone Calculator — Music Frequency & Interval
In equal temperament, each octave contains 12 equal semitones and each semitone multiplies frequency by 2^(1/12) ≈ 1.0595. Enter two frequencies to find the semitones between them, or enter a starting frequency and semitone count to find the target pitch.
Mode
Hz
Hz
Number of semitones from f₁ to f₂ in equal temperament
- 1
Frequency ratio
f₂ ÷ f₁ = 880 ÷ 440 = 2 - 2
log₂(ratio)
log₂(2) = 1Logarithm base 2 gives the number of octaves between the frequencies. - 3
Semitones
12 × 1 = 12
How does this calculator work?
Semitones = 12 × log₂(f₂/f₁) to find the interval between two frequencies. Target frequency = f₁ × 2^(n/12) to go n semitones from a reference. Each semitone is a 2^(1/12) ≈ 1.0595 ratio; 12 semitones = one octave (2× frequency). 100 cents = 1 semitone.
Formula
How this is calculated
The Western equal-temperament scale divides each octave (a 2:1 frequency ratio) into 12 equal semitones. Because the divisions are logarithmic, each semitone multiplies frequency by the twelfth root of 2: 2^(1/12) ≈ 1.059463. An octave up doubles the frequency (12 semitones × 2^(1/12) = 2); an octave down halves it.
Given two frequencies, the number of semitones between them is n = 12 × log₂(f₂/f₁). Positive values mean f₂ is higher; negative values mean it is lower. One semitone equals 100 cents — a finer unit used for tuning (1 cent = 1/100 of a semitone). Given a starting frequency and a semitone count, the target frequency is f₁ × 2^(n/12).
This calculator uses 12-tone equal temperament (12-TET), which is standard for modern keyboards and most Western music. Other tuning systems (just intonation, meantone, 19-TET, 31-TET) use different intervals and the results here will not apply to them. Frequency values assume standard concert pitch (A4 = 440 Hz); if your reference is different, adjust f₁ accordingly.
Frequently asked questions
Exactly 12 semitones — for example from A4 (440 Hz) to A5 (880 Hz). Each semitone is a 2^(1/12) ≈ 1.0595 frequency ratio; twelve of them multiply together to give 2, doubling the frequency.
1 semitone = 100 cents. Cents are used for fine tuning differences: a perfectly tuned piano has 0 cents deviation, while two musicians playing 5 cents apart will produce audible beating. Use semitones for musical intervals; use cents for precision tuning measurements.
A perfect fifth is 7 semitones, giving a ratio of 2^(7/12) ≈ 1.4983 — very close to the just ratio of 3/2 = 1.5000 but not identical. This slight compromise is what lets equal-temperament keyboards play in all keys without retuning.
Also known as
TG we-Calculate Editorial Team. (2026). Semitone Calculator — Music Frequency & Interval [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/semitone-calculator
TG we-Calculate Editorial Team. "Semitone Calculator — Music Frequency & Interval." TG we-Calculate. 2026. https://we-calculate.com/calculator/semitone-calculator.
TG we-Calculate Editorial Team, "Semitone Calculator — Music Frequency & Interval," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/semitone-calculator
@misc{wecalculate_semitone_calculator, title = {Semitone Calculator — Music Frequency & Interval}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/semitone-calculator}}, year = {2026}, note = {TG we-Calculate} }
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