Cents Between Frequencies Calculator
Calculate the musical interval in cents between two frequencies in Hz. 100 cents = 1 semitone; 1200 cents = 1 octave.
How to use this tool
- Enter frequency 1 and frequency 2 in the fields above.
- Results update instantly as you type — or click Calculate.
- Read your interval and the full breakdown beneath it.
Measure the pitch distance between two frequencies in cents (1200 cents = one octave).
Formula
Cents = 1200 × log2(f2 / f1)
Semitones = cents ÷ 100 | Ratio = f2 / f1
How it works
This calculator expresses the musical interval between two frequencies as cents — thousandths of a semitone — using the logarithmic relationship between frequency ratios and perceived pitch. Because pitch perception is logarithmic, doubling the frequency always produces exactly 1200 cents (one octave) regardless of the starting pitch.
The result is signed: a negative value means f2 is lower than f1. Accuracy depends on the precision of the input frequencies; the formula itself is exact for 12-tone equal temperament.
Worked example
Worked example
- f1 = 440 Hz (A4), f2 = 880 Hz (A5).
- Ratio = 880 / 440 = 2.
- Cents = 1200 × log₂(2) = 1200 × 1 = 1200 ¢.
- Semitones = 1200 / 100 = 12 st.
Interval: 1200 ¢ | Semitones: 12 st | Ratio: 2
Key terms
- Cent (¢)
- One hundredth of a semitone; the standard unit for measuring small pitch differences. 1200 cents = one octave.
- Frequency ratio
- The quotient of two frequencies. A ratio of 2 represents one octave; a ratio of 2^(1/12) ≈ 1.0595 represents one semitone in equal temperament.
- Equal temperament
- A tuning system that divides the octave into 12 equally spaced semitones, each with a frequency ratio of 2^(1/12).
- Logarithm base 2 (log₂)
- The power to which 2 must be raised to equal a given number. Used in pitch calculations because doubling frequency always produces an octave.
- Interval
- The musical distance between two pitches, measured in semitones, cents, or named intervals such as a fifth or an octave.
Frequently asked questions
- How many cents is one semitone?
- Exactly 100 cents. An octave spans 1200 cents (12 × 100).
- How do I use this for tuning?
- Enter the reference pitch and the measured pitch. If cents offset is within ±5 ¢ the instrument is in tune.