Frequency Ratio to Cents Converter
The cent is the standard logarithmic unit for measuring musical intervals, with exactly 1,200 cents to the octave and 100 cents to an equal-tempered semitone. This tool converts any frequency ratio, or a pair of frequencies in hertz, into cents. It is the right way to compare intervals from just intonation, equal temperament, and historical tunings, because equal numbers of cents always sound like equal intervals regardless of register. Enter a lower and higher frequency, or set the lower to 1 to enter a ratio directly.
Cents from frequency ratio formula
ratio = f_high / f_low
cents = 1200 * log2(ratio)
cents = 1200 * ln(ratio) / ln(2)
semitones = cents / 100
octaves = cents / 1200
The cent is defined so that one octave (a ratio of 2) equals 1,200 cents and an equal-tempered semitone equals 100 cents. Because the relationship is logarithmic, equal cent counts represent equal-sounding intervals at any pitch.
Interval reference points
- Octave: ratio 2:1 = 1,200 cents exactly.
- Just perfect fifth: ratio 3:2 = 701.955 cents.
- Just perfect fourth: ratio 4:3 = 498.045 cents.
- Just major third: ratio 5:4 = 386.314 cents.
- Equal-tempered semitone: ratio 2^(1/12) = 100 cents exactly.
Cents conversion: frequently asked questions
What is a cent in music?
A cent is a logarithmic unit of musical interval. By definition there are 1,200 cents in one octave, and an equal-tempered semitone is exactly 100 cents. Because pitch perception is logarithmic, cents let you compare intervals from different tuning systems on a single linear scale.
What is the formula for cents from a frequency ratio?
Cents equal 1,200 times the base-2 logarithm of the frequency ratio: cents = 1200 * log2(f2 / f1). Equivalently, cents = 1200 * ln(ratio) / ln(2). A ratio of 2 (one octave) gives exactly 1,200 cents; a ratio of 1 gives 0 cents.
How many cents is a just perfect fifth?
A just perfect fifth has the ratio 3:2. Plugging into the formula gives 1200 * log2(1.5) = 701.955 cents. The equal-tempered fifth is 700 cents, so the just fifth is about 1.955 cents sharp of equal temperament.
Can I enter two frequencies instead of a ratio?
Yes. Enter the lower frequency and the higher frequency in hertz and the calculator forms the ratio (higher divided by lower) before converting to cents. You can also enter a ratio directly by setting the lower frequency to 1.
Why are cents better than hertz for comparing intervals?
Hertz differences are not perceptually equal across the range: 100 Hz is a large interval near 200 Hz but tiny near 4,000 Hz. Cents are ratio-based, so the same number of cents always sounds like the same interval regardless of register, matching how the ear works.
Official sources
- National Institute of Standards and Technology: SI units and frequency.
- Acoustical Society of America: acoustics and musical interval standards.
Reviewed by the CalculatorHub team, edited by James Graham, 16 June 2026. See our methodology.