Cents to Frequency Ratio Calculator
A cent is a logarithmic unit of pitch: 100 cents to an equal-tempered semitone and 1,200 cents to an octave. This calculator converts cents to a frequency ratio using the exact definition, ratio equals 2 to the power of cents over 1,200, and back to cents from the ratio. Enter a number of cents and a base frequency, and it returns the frequency ratio, the resulting pitch, and the round-trip cents so you can verify the conversion. It is useful for fine tuning, microtonal work, and measuring how sharp or flat a pitch is.
Cents and ratio formula
frequency ratio = 2 ^ (cents / 1200)
resulting pitch = base frequency * ratio
cents from ratio = 1200 * log2(ratio)
semitones = cents / 100
The definition fixes 1,200 cents to an octave (ratio 2) and 100 cents to an equal-tempered semitone. The conversion is exact and reversible, so the cents-from-ratio check returns your input.
Cents context
- 100 cents is one equal-tempered semitone (ratio about 1.0595).
- 1,200 cents is a full octave (ratio exactly 2).
- 700 cents is an equal-tempered perfect fifth (ratio about 1.4983).
- A just perfect fifth (ratio 3 to 2) is about 701.96 cents.
- Cents are logarithmic, matching how we perceive pitch intervals.
Cents and ratios: frequently asked questions
What is a cent in music?
A cent is a unit of pitch interval defined so that one equal-tempered semitone equals exactly 100 cents and an octave equals 1,200 cents. It is logarithmic, which means equal cent differences correspond to equal pitch ratios regardless of the starting frequency. Cents are used to measure fine tuning differences.
How do I convert cents to a frequency ratio?
The frequency ratio equals 2 raised to the power of cents divided by 1,200. For example, 1,200 cents gives 2 to the power 1, which is 2, an octave. 100 cents gives 2 to the power one-twelfth, about 1.0595, one equal-tempered semitone. This calculator computes the ratio exactly from this definition.
How do I go from a ratio back to cents?
Cents equal 1,200 times the base-2 logarithm of the ratio. This calculator reports the cents for the ratio you build, so you can check that your forward and reverse values agree. The relationship is exact and reversible.
How does this give a resulting pitch?
If you enter a base frequency, the calculator multiplies it by the frequency ratio to give the pitch that lies the entered number of cents above (or below, for negative cents) the base. This is handy for retuning, microtonal work, or checking how far off a measured pitch is.
Why are cents logarithmic?
Pitch perception is roughly proportional to the logarithm of frequency, so equal musical intervals correspond to equal frequency ratios, not equal frequency differences. Defining cents on a base-2 logarithm makes an octave a fixed 1,200 cents anywhere in the range, matching how we hear intervals.
Official sources
- NIST: Unit and Logarithmic Definitions.
- U.S. National Institute of Standards and Technology: Time and Frequency Reference.
Reviewed by the CalculatorHub team, edited by James Graham, 16 June 2026. See our methodology.