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Note Frequency Calculator

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Every pitch in equal temperament is the twelfth root of two times the one below it, so the whole system hangs off a single reference — conventionally A above middle C at 440 Hz, though Baroque ensembles use 415 and plenty of orchestras use 442. Enter a note to get its frequency, or a measured frequency to get the nearest note and how many cents off it is, at whatever reference you set.

What do you have?

A letter, an optional # or b, and the octave — A4, C#3, Bb5

440 Hz is the ISO standard, but it is a convention rather than a law

Try:

How to use the note frequency calculator

  1. 1Choose whether you have a note name or a frequency.
  2. 2For a note, write the letter, an optional sharp or flat, and the octave — A4, C#3, Bb5.
  3. 3For a frequency, enter it in hertz; the nearest note and the cents deviation come back.
  4. 4Set the tuning reference if you are not at concert pitch.
  5. 5Use the interval table to see how far equal temperament sits from the pure ratios it approximates.

Examples

The reference itself

Input
A4
Result
440 Hz, MIDI note 69

The note every other frequency in the system is derived from.

Middle C

Input
C4
Result
261.63 Hz, MIDI note 60

Not a round number, because it is nine semitones below the reference rather than the reference itself.

A slightly flat string

Input
434 Hz
Result
A4, 23.8 cents flat

Cents rather than hertz, because the same number of hertz is a much larger interval at the bottom of the range than the top.

About the note frequency calculator

The exponential that holds it together

An octave is a doubling of frequency, and that much is a fact about hearing rather than a convention: notes an octave apart sound like versions of the same note in every musical culture that has been studied. Equal temperament divides that doubling into twelve equal ratios, so each semitone is the twelfth root of two — about 1.0595, or a 5.95% rise in frequency.

Because the steps are equal in ratio rather than in hertz, the absolute spacing grows as you go up. The semitone from A4 to A#4 is 26 Hz wide; the same semitone an octave higher is 52 Hz, and an octave lower it is 13. That is why a piano's strings are not evenly graded in length, and why frets on a guitar crowd together towards the body.

The exponential also explains why tuning by ear works the way it does. What the ear compares is the ratio between two pitches, not their difference, so an interval sounds the same wherever it is played. Beat frequencies — the slow pulsing heard when two nearly-identical pitches sound together — are the tool that turns that ratio comparison into something countable, which is how a piano is tuned without any electronics at all.

What the tuning reference does and does not change

Changing the reference moves every pitch by the same ratio, so all the intervals are preserved and a piece played at 415 sounds like the same piece slightly lower. Nothing musical about the relationships changes. What does change is the tension on strings, the response of wind instruments, and the range a singer is comfortable in — which is exactly why the argument about pitch standards has run for three hundred years and is really an argument about instruments and voices rather than about arithmetic.

The 432 Hz reference has attracted a body of claims about resonance and wellbeing that have no evidential support, and it is worth being plain that this page takes no position beyond the arithmetic. Setting the reference to 432 lowers everything by about 32 cents, which is roughly a third of a semitone and audible to most listeners as a slight flatness against concert pitch. That is the whole of what it does.

For practical purposes the reference matters most when instruments have to play together. A wind instrument's pitch is fixed by its bore and rises as it warms up; a string instrument can be tuned anywhere but the strings were designed for a particular tension. An orchestra tuning to 443 rather than 440 is making a small collective decision about brightness, and every player has to make the same one.

Frequently asked questions

Why is A 440 Hz rather than something rounder?
Because it was a negotiated compromise rather than a derivation. Pitch standards drifted upwards for centuries as ensembles tuned sharp to sound brighter, and references between 415 and 460 all saw serious use. An international conference settled on 440 in 1939 and the ISO codified it in 1955. It is a convention that everybody agreed to, not a property of anything — which is why period-instrument groups can reasonably use 415 and many European orchestras still tune to 442 or 443.
What is a cent, and why not just use hertz?
A cent is a hundredth of a semitone measured as a ratio — the 1200th root of two, or about 0.058%. Hertz would be useless for describing how far out of tune something is, because pitch is logarithmic: ten hertz is nearly half a semitone at the bottom of a double bass and barely a twentieth of one at the top of a piccolo. Cents describe the same musical interval anywhere in the range, which is why every tuner reports them.
Why does the interval table show tempered notes as slightly wrong?
Because they are, and deliberately so. The intervals the ear hears as consonant are small whole-number ratios — 3:2 for a fifth, 5:4 for a major third — and those ratios cannot be stacked into a twelve-note scale that closes on itself. Equal temperament spreads the discrepancy evenly, so every fifth is two cents narrow and every major third is fourteen cents wide. The price is that nothing is quite pure; the reward is that every key sounds the same and a fixed-pitch instrument can play in all of them.
What are MIDI note numbers?
An integer for every semitone, running from 0 at C-1 to 127 at G9, with 60 as middle C and 69 as A4. They are how electronic instruments address pitch internally, and they make the arithmetic straightforward: the frequency of note n is 440 times two to the power of (n − 69) over 12. The number carries no tuning information, which is why the same MIDI file plays at 440 or 415 depending only on what the receiving instrument is set to.
Are sharps and flats really the same note?
In equal temperament, yes — F# and Gb are the same key on a piano and the same frequency here. In other tuning systems they are not, and on instruments with flexible pitch they are still not: string players and singers tend to place a leading note higher than its enharmonic equivalent, following the harmonic sense of the passage. Equal temperament collapses that distinction, which is one of the things it trades away for universal key compatibility.

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