What is a cent in music?

A cent is a logarithmic unit for measuring musical intervals. There are 100 cents in a semitone and 1200 cents in an octave. The cent scale allows precise measurement of pitch differences too small to name with standard interval names.

What is the formula for converting cents to a frequency ratio?

The formula is: ratio = 2^(cents / 1200). For example, 700 cents (a perfect fifth in equal temperament) gives ratio = 2^(700/1200) ≈ 1.4983.

How do I convert a frequency ratio to cents?

Use the inverse formula: cents = 1200 × log2(ratio) = 1200 × ln(ratio) / ln(2). For example, the just perfect fifth ratio 3:2 = 1.5 gives cents = 1200 × log2(1.5) ≈ 701.96 cents.

Why is 1200 used in the formula?

An octave represents a frequency ratio of exactly 2:1. The cent system divides the octave into 1200 equal logarithmic steps (12 semitones × 100 cents each), so 1200 cents always equals a ratio of 2.

What is the difference between equal temperament and just intonation?

Equal temperament divides the octave into 12 equal semitones (100 cents each), giving irrational ratios. Just intonation uses simple integer ratios tuned to the harmonic series. For example, the just perfect fifth is exactly 3:2 (≈701.96 cents), while the equal-tempered perfect fifth is exactly 700 cents (≈1.4983 ratio).

Can I enter a ratio as a fraction like 3/2?

Yes. The calculator accepts both decimal values (e.g. 1.5) and fraction notation (e.g. 3/2) in the ratio field.

Cents to Ratio Calculator

Name: Cents to Ratio Calculator
Availability: InStock
Author: Nham Vu

Enter cents to get the frequency ratio, or enter a ratio to get cents — uses the standard formula ratio = 2^(cents/1200).

Conversion Input

Direction

Cents value

Range: any value (negative = downward interval)

Common presets

Enter a value and click Convert

or choose a preset on the left

Copied!

Summary

Enter cents to get the frequency ratio, or enter a ratio to get cents — uses the standard formula ratio = 2^(cents/1200).

How it works

Select the conversion direction: Cents to Ratio or Ratio to Cents.
Enter a value in the input field.
Click Convert to calculate the result instantly.
Use the common presets to quickly load standard interval values.
Click Copy to copy the result to your clipboard.

Use cases

Music theorists converting just intonation ratios to cent values for analysis.
Composers and arrangers comparing equal temperament vs. just intonation intervals.
Instrument builders and tuners calculating precise pitch deviations in cents.
Audio software developers implementing pitch-shifting and tuning algorithms.
Students studying music theory and acoustics who need to verify interval calculations.
Synthesizer programmers working with pitch bend or detuning values.

Frequently Asked Questions

Last updated: 2026-07-01 · Reviewed by Nham Vu