Cents Tuning Calculator
Measures the pitch interval between two frequencies in cents, the standard unit for fine tuning. Use it to quantify how sharp or flat an instrument or note is relative to a reference pitch.
About this calculator
A cent is one hundredth of a semitone, making it the standard unit for expressing small pitch differences in music. Because human pitch perception is logarithmic, the formula uses a base-2 logarithm: Cents = 1200 × log₂(f₂ / f₁), where f₁ is the reference frequency and f₂ is the target frequency. A result of +100 cents means exactly one semitone sharp, −50 cents means a quarter-tone flat. The factor of 1200 comes from the fact that one octave (a 2:1 frequency ratio) equals exactly 1200 cents in equal temperament. This formula works for any two frequencies, regardless of scale or tuning system, making it useful for comparing just intonation intervals, synthesizer detuning, and microtonal composition. Most professional tuners display offsets in cents because it gives a universal, scale-independent measure of intonation accuracy.
How to use
Suppose a violinist is playing what should be concert A at 440 Hz, but their note measures 446 Hz. Enter f₁ = 440 Hz and f₂ = 446 Hz. The calculation is: Cents = 1200 × log₂(446 / 440) = 1200 × log₂(1.01364) = 1200 × 0.01951 ≈ 23.4 cents. The note is approximately 23 cents sharp — nearly a quarter-tone too high. The violinist should relax the string tension slightly to bring the pitch back to 440 Hz.
Frequently asked questions
How many cents equal one semitone in equal temperament?
Exactly 100 cents equal one semitone in 12-tone equal temperament (12-TET). The octave is divided into 12 equal semitones, and since one octave spans 1200 cents, each semitone is 100 cents wide. This means a pitch difference of 50 cents is a quarter-tone, and 200 cents is a whole tone. Most listeners can detect pitch differences as small as 5–10 cents, while highly trained musicians can notice deviations of 2–3 cents.
What does a negative cents value mean in tuning?
A negative cents value means the target frequency f₂ is lower in pitch than the reference frequency f₁ — in other words, the note is flat. For example, −15 cents means the measured pitch is 15 cents below the reference, which is a noticeable but not dramatic flatness. In instrument tuning and intonation correction, negative values indicate the performer or instrument needs to raise the pitch. Synthesizer detune controls also use positive and negative cent offsets to create chorus-like thickening effects by layering slightly detuned voices.
Why is the cents formula based on a logarithm rather than a simple ratio?
Human pitch perception is logarithmic, not linear — we perceive equal musical intervals as equal ratios of frequency rather than equal differences. For example, going from 220 Hz to 440 Hz feels like the same interval as going from 440 Hz to 880 Hz, even though the first jump is 220 Hz and the second is 440 Hz. Using log₂ converts these multiplicative ratios into additive, linear cent values that match our perceptual experience. This makes it straightforward to add, subtract, and compare intervals without worrying about the absolute frequencies involved.