Cent to Frequency Calculator: Convert Cents to Hz
- Frequency ratio
- Result
- Cents
- 100 cents
- You entered
- Reference frequency
- 440 Hz
- You entered
This calculator converts a musical interval in cents to a frequency ratio, and then to a target frequency in hertz (Hz) when you provide a starting frequency. Enter the number of cents (positive for higher, negative for lower) and a reference frequency (the starting pitch), and you get the exact frequency of the note that many cents away, plus the frequency ratio.
Formula
The cent system divides one octave into 1200 equal logarithmic steps. The formula for the target frequency is:
f = f₀ × 2^(cents / 1200)
- f – target frequency in hertz (Hz)
- f₀ – reference (starting) frequency in hertz (Hz)
- cents – interval size in cents (can be positive or negative)
The frequency ratio is simply 2^(cents/1200). A cent is one hundredth of a semitone, and there are 12 semitones per octave, so 1200 cents per octave.
Worked Example
Using the default values: cents = 100, reference frequency = 440 Hz.
- Calculate the exponent: 100 / 1200 = 0.083333…
- Compute 2^0.083333 = 1.059463…
- Multiply by the reference: 440 × 1.059463 = 466.1638 Hz
The result is 466.16 Hz (rounded to 4 decimal places). This is exactly the frequency of C#4 when A4 = 440 Hz, because 100 cents is one semitone.
Why Cents Matter in Music
Cents are a logarithmic unit of pitch interval. They are used because human hearing perceives pitch logarithmically: a difference of 100 cents sounds the same size regardless of where it occurs in the scale. This makes cents ideal for describing tuning adjustments, chord voicings, and microtonal intervals.
For example, a difference of 50 cents is a quarter tone, and 1200 cents is exactly one octave (doubling the frequency). The cent system is standard in music theory, instrument tuning, and digital audio software.
How to Use This Calculator
Enter the interval in cents (positive for higher, negative for lower) and the reference frequency. The calculator returns the target frequency and the ratio. Common uses:
- Find the frequency of a note that is a certain number of cents away from a known pitch.
- Convert a tuning offset (e.g., +50 cents) to an actual frequency for a synth or sampler.
- Check the frequency of a note after applying a pitch bend or vibrato depth.
For example, to find the frequency of a note 200 cents above 440 Hz, enter 200 and 440. The result is 440 × 2^(200/1200) = 493.88 Hz (B4).
Common Mistakes and Limitations
The most common mistake is forgetting that cents are logarithmic, not linear. Adding 100 cents to a frequency does not add a fixed number of hertz; it multiplies the frequency by a fixed ratio. Another mistake is confusing cents with semitones: 1 semitone = 100 cents, so 50 cents is half a semitone.
This calculator assumes equal temperament, where each semitone is exactly 100 cents. In other tuning systems (just intonation, Pythagorean), the cent values of intervals differ. The formula is mathematically exact for equal temperament.
Also note that the calculator works for any frequency, but typical musical ranges are between 20 Hz and 20,000 Hz (the human hearing range).
Frequently Asked Questions
How many cents are in a semitone?
Exactly 100 cents. A semitone is the smallest interval in standard Western music (e.g., from C to C#).
How many cents are in an octave?
1200 cents. An octave doubles the frequency, and 2^(1200/1200) = 2.
What is the frequency of a note 50 cents above 440 Hz?
440 × 2^(50/1200) ≈ 452.89 Hz. This is a quarter tone above A4.
Can I convert cents to hertz without a reference frequency?
No, because cents measure an interval, not an absolute pitch. You need a starting frequency to get a target frequency. The calculator also gives the ratio, which is independent of the reference.
What is the difference between cents and hertz?
Hertz measures absolute frequency (cycles per second). Cents measure the relative size of an interval on a logarithmic scale. The same cent interval corresponds to different hertz differences depending on the starting pitch.
Why is 1200 cents per octave?
Because there are 12 semitones per octave, and each semitone is divided into 100 cents. This makes 12 × 100 = 1200.