This calculator converts a pitch change in cents into hertz. Enter the starting frequency and the change in cents (100 cents is one equal-tempered semitone, negative for lower); you get the new frequency and the frequency ratio.
Formula
f₂ = f₁ × 2^(c ÷ 1200). An octave (ratio 2) is 1,200 cents, so one cent is a ratio of 2^(1/1200) ≈ 1.000578.
- f₁: starting frequency in hertz (A4 is often 440 Hz)
- c: change in cents, positive up, negative down
Worked Example
A4 = 440 Hz raised by 100 cents.
- Ratio = 2^(100 ÷ 1200) = 2^(1/12) = 1.059463
- f₂ = 440 × 1.059463 = 466.16 Hz (A♯4/B♭4)
How to read the result
Tuners show how many cents a note is sharp or flat; this turns that into hertz. A string 5 cents flat of 440 Hz is at about 438.73 Hz. To go the other way, cents = 1200 × log₂(f₂ ÷ f₁).
Limits and common mistakes
- Cents are logarithmic: 50 cents up then 50 down returns exactly to the start, but the hertz steps are not equal.
- The 100-cent semitone is equal temperament; just intervals differ by a few cents.
Frequently Asked Questions
How many cents in a semitone?
100 in equal temperament.
How many hertz is 1 cent at 440 Hz?
About 0.254 Hz.
What is 440 Hz lowered by 1,200 cents?
220 Hz, one octave down.
How do I convert hertz to cents?
cents = 1200 × log₂(f₂ ÷ f₁).
Formula used
in f1 | Starting frequency | Hz | 440 | 0 | 100000 in c | Change | cents | 100 | -12000 | 12000 out f2 | New frequency | Hz | f1 * 2^(c / 1200) | 2 out ratio | Frequency ratio | - | 2^(c / 1200) | 6
Each line is one input (in, sel, list) or one result (out: label, unit, formula, decimals). How the calculators work
Method: the standard formula for this calculation, rounded as each result states. See how the calculators work or report an error.