What is a cent in music?

A cent is 1/100th of a semitone in equal temperament, making it 1/1200th of an octave. The word comes from the Latin centum (one hundred). Because human pitch perception is roughly logarithmic, cents provide a perceptually linear unit: moving 10 cents always sounds like the same tiny interval regardless of register.

What is the formula to convert cents to frequency?

f2 = f1 x 2^(cents / 1200). The ratio 2^(1/1200) is the frequency multiplier for a single cent. To reverse it: cents = 1200 x log2(f2 / f1). Both formulas follow from the equal-temperament definition where the octave (factor of 2) is divided into 1200 equal logarithmic steps.

How many cents is a semitone, a tone, and an octave?

One semitone = 100 cents. One whole tone (major second) = 200 cents. A perfect fifth = 700 cents. An octave = 1200 cents. These are equal-temperament values; just-intonation intervals differ by a few cents (e.g. a just perfect fifth is 701.96 cents, about 2 cents wider than equal temperament).

How accurate are cents for measuring tuning deviation?

Very accurate for practical purposes. Most trained listeners can detect deviations of 5-10 cents; professional orchestral tuning tolerates roughly plus or minus 5 cents. Electronic tuners typically resolve to 1 cent, which corresponds to a frequency change of about 0.058% — for A4 (440 Hz) that is approximately 0.25 Hz per cent.

What is the A4 reference frequency and why does it matter?

A4 is the note A in the fourth octave (MIDI 69), used as the universal tuning reference. Modern concert pitch is standardised at 440 Hz (ISO 16 / 1975). Earlier periods used different references: Baroque ensembles often tuned to 415 Hz (a semitone lower), some orchestras use 441-443 Hz for a brighter sound, and historically documented pitches range from about 380 Hz to 465 Hz. Changing the A4 reference shifts every calculated frequency proportionally.

How do I convert a MIDI note number to a frequency?

Use the formula f = A4 x 2^((n - 69) / 12) where n is the MIDI note number and A4 is your tuning reference (default 440 Hz). MIDI note 69 = A4, MIDI 60 = middle C (C4), MIDI 0 = C-1 at about 8.18 Hz, and MIDI 127 = G9 at about 12 544 Hz.

Cents to Frequency Calculator

The cents-to-frequency calculator converts pitch intervals expressed in cents into exact hertz values — and reverses the process so you can measure how far apart any two frequencies really are. It covers three workflows in one tool: apply a cent offset to a base frequency, compute the cent interval between two frequencies, and look up any MIDI note number.

How it works

Sound pitch is perceived logarithmically: doubling a frequency raises pitch by exactly one octave, regardless of the starting note. Equal temperament divides that octave into 12 semitones, and each semitone into 100 cents, giving 1 200 cents per octave. The defining formula is:

f2 = f1 × 2^(cents ÷ 1200)

Because the exponent grows linearly with cents and the result is a power of 2, every equal-temperament interval is expressed precisely. To reverse the operation — measuring the interval between two known frequencies — rearrange to:

cents = 1 200 × log₂(f2 ÷ f1)

The MIDI mode uses the same formula anchored at MIDI note 69 (A4):

f = A4 × 2^((MIDI − 69) ÷ 12)

All three formulas are evaluated in IEEE-754 double precision directly in your browser; no data leaves your device.

Worked example

You have a 440 Hz tone (A4) and want to find the note 700 cents above it — a perfect fifth in equal temperament:

Plug in: f2 = 440 × 2^(700 ÷ 1200) = 440 × 2^(0.5833…) ≈ 440 × 1.4983 ≈ 659.26 Hz
That is E5 in equal temperament (MIDI note 76), the standard concert pitch for the note a fifth above A4.
In just intonation the perfect fifth has a frequency ratio of exactly 3:2 = 1.5000, giving 440 × 1.5 = 660 Hz — about 1.96 cents sharper than the equal-tempered value.

Base	Cents	Semitones	Ratio	Result
440 Hz	100	1	1.0595	466.16 Hz (A#4)
440 Hz	700	7	1.4983	659.26 Hz (E5)
440 Hz	1200	12	2.0000	880.00 Hz (A5)
261.63 Hz	400	4	1.2599	329.63 Hz (E4)
659.26 Hz	-700	-7	0.6674	440.00 Hz (A4)

Formula note

The formula f2 = f1 × 2^(cents ÷ 1200) is the direct consequence of equal temperament’s definition: the octave ratio of 2 is divided into 1 200 equal logarithmic steps. Setting cents = 100 gives the semitone ratio 2^(1/12) ≈ 1.059 463. Setting cents = 1 200 gives 2^1 = 2.000 000, the exact octave. Setting cents = 0 gives 2^0 = 1, a perfect unison. The logarithmic inverse cents = 1 200 × log₂(f2/f1) is exact for any positive frequency pair; the calculator also decomposes the result into octaves, whole semitones, and remaining cents for easier reading.