What is a cent in music?

A cent is a logarithmic unit for measuring musical intervals. There are 100 cents per semitone and 1200 cents per octave. Because our perception of pitch is logarithmic, cents provide a uniform scale for comparing interval sizes.

What is the formula to convert two frequencies to cents?

cents = 1200 × log₂(f2 / f1). For example, A4 (440 Hz) to A5 (880 Hz) gives 1200 × log₂(880/440) = 1200 × log₂(2) = 1200 cents (one octave).

How do I convert cents back to a frequency?

f2 = f1 × 2^(cents / 1200). If the base frequency is 440 Hz and you want +700 cents (a perfect fifth), then f2 = 440 × 2^(700/1200) ≈ 659.26 Hz.

What is the difference between a frequency ratio and two frequencies?

A frequency ratio (e.g. 3/2) is a single number that describes the relationship between two pitches. Two frequencies (e.g. 440 Hz and 660 Hz) give the same ratio when divided: 660/440 = 1.5 = 3/2. Both encode the same interval; this tool lets you work with either form.

Why does the tool use log base 2?

An octave always doubles the frequency (ratio 2:1). Using log₂ maps that doubling to exactly 1200 cents. Any other base would require a scaling constant, making the formula less intuitive.

Can I enter fractional or negative cent values?

Yes. Negative cents mean the target frequency is below the base. For example, −100 cents lowers the pitch by one semitone. Fractional cents like 50.5 are also valid and commonly used in microtonal music.

Frequency To Cents

Enter two frequencies in Hz (or a ratio) to get the interval in cents, or enter cents plus a base frequency to find the target frequency.

Conversion Input

Mode

Base frequency f1 (Hz)

Target frequency f2 (Hz)

Common intervals

Enter values and click Convert

or pick an interval preset on the left

Copied!

Summary

This tool converts between frequencies (in Hz) and musical cents using the formula cents = 1200 × log₂(f2 / f1). You can work in three modes: compare two Hz values, enter a plain frequency ratio, or reverse the process by providing a cent value and base frequency to calculate the resulting pitch. Results include the equivalent semitones and octaves for quick music-theory reference.

How it works

Select a conversion mode: Two Frequencies, Ratio to Cents, or Cents to Frequency.
Enter the required values in the input fields.
Click Convert (or press Enter) to compute the result instantly.
Use the common interval presets to quickly load typical cent or ratio values.
Copy the result to your clipboard with the Copy button.

Use cases

Measure the pitch difference in cents between any two sine waves or recorded notes.
Tune synthesizer oscillators precisely by converting Hz offsets to cent detuning.
Verify just-intonation tunings by comparing Hz ratios against cent values.
Calculate the target frequency for a pitch-shifted note in audio production.
Confirm microtuning intervals when designing alternative scales.
Analyze the tuning error of a physical instrument against equal temperament.
Convert hardware oscillator frequency readings to musical cent values for DAW automation.
Teach music acoustics by showing the logarithmic relationship between frequency and pitch.

Frequently Asked Questions

Last updated: 2026-05-29 · Reviewed by Nham Vu