Frequency to Pitch Calculator
Convert any audio frequency in Hz to its position in cents relative to a reference pitch (default A4 = 440 Hz). Use it for tuning instruments, analysing intonation, or exploring alternate tuning systems.
About this calculator
The musical relationship between two frequencies is measured in cents, where 100 cents equals one equal-tempered semitone and 1,200 cents equals one octave. The formula is: cents = 1200 × log₂(f / f_ref), where f is the measured frequency and f_ref is the reference frequency (commonly A4 = 440 Hz). A positive result means the measured pitch is sharp; negative means flat. Because the formula uses a base-2 logarithm, it maps the exponential nature of frequency doubling onto a linear musical scale. This is essential for tuning — a deviation of ±5 cents is barely perceptible, while ±20 cents sounds noticeably out of tune. Alternate tuning systems such as A4 = 432 Hz or 415 Hz simply change f_ref, shifting the entire pitch map accordingly.
How to use
Suppose you measure a string vibrating at 450 Hz and your reference is A4 = 440 Hz. Apply the formula: cents = 1200 × log₂(450 / 440) = 1200 × log₂(1.02273). log₂(1.02273) = ln(1.02273) / ln(2) ≈ 0.02248 / 0.6931 ≈ 0.03244. Multiply: 1200 × 0.03244 ≈ 38.9 cents. The string is approximately 39 cents sharp — nearly a half-semitone above A4 — so you would loosen the tuning peg slightly to bring it back to 0 cents (440 Hz).
Frequently asked questions
How many cents deviation can the human ear detect when tuning an instrument?
Most trained musicians can detect pitch differences of around 5–10 cents, while highly trained listeners or those with perfect pitch may hear deviations as small as 2–3 cents. In practice, instruments are considered acceptably in tune when within ±10 cents of the target frequency. Ensemble playing is more sensitive — even 15 cents of deviation between two instruments playing the same note creates an audible beating effect that sounds out of tune. Strobe tuners and software tuners typically measure to ±1 cent precision, well within the resolution needed for professional tuning.
What is the difference between equal temperament and just intonation when converting frequency to pitch?
In equal temperament, each of the 12 semitones divides the octave into exactly equal frequency ratios (the 12th root of 2, ≈ 1.05946), making every key equally in tune at the cost of slight compromises on pure intervals. Just intonation uses small whole-number frequency ratios (e.g. a perfect fifth = 3/2 = 1.5) that sound pure and beatless but cause certain keys to sound out of tune when modulating. The cents formula works for both systems — you simply compare the measured frequency against the just-intonation target frequency rather than the equal-tempered one. Many string players and vocalists naturally gravitate toward just intonation when performing without accompaniment.
Why is A4 = 440 Hz used as the standard reference frequency for tuning?
A440 was standardised by the International Organization for Standardization (ISO) in 1955 and reaffirmed in 1975, providing a universal reference for instrument manufacturers, orchestras, and electronics worldwide. Before standardisation, pitch varied significantly between countries and eras — baroque orchestras often tuned to A415 Hz, approximately a semitone lower. Today, some orchestras (particularly in Europe) tune to A441 or A442 for a slightly brighter sound, and some musicians prefer A432 Hz for various aesthetic reasons. The cents formula accommodates any reference frequency, so you can calculate deviations relative to whichever standard applies to your context.