Note frequency chart every piano key in hertz, and any hertz as a note

Note frequency chart: the octave around middle C

The table below gives the frequency of every note in the fourth octave, from middle C to B4, at the two reference pitches people ask about most: the standard A4 = 440 Hz and the alternative A4 = 432 Hz. Each row is about 5.95 % higher than the row above it, and the next C (C5) is exactly double C4.

Sharps and flats share a key on the piano, so C♯ and D♭ have the same frequency in equal temperament. The chart lists them once.

To get any other octave, double the frequency for each octave up and halve it for each octave down. E4 is 329.63 Hz, so E5 is 659.26 Hz and E3 is 164.81 Hz. The interactive piano above shows all 88 keys with their frequencies, switches the reference between 440, 432 and 415 Hz, converts any frequency in hertz into the nearest note with its offset in cents, and lists the full chart for octaves 0 to 8.

Piano key frequencies: the C and A of every octave

The quickest way to find your bearings on the keyboard is to remember two notes per octave. Every A at standard pitch is a round number (27.5, 55, 110, 220, 440, 880 Hz and so on), because A4 is the reference and each octave doubles it. The Cs are where octave numbers change: in scientific pitch notation, the note after B3 is C4, not C3.

Piano keys are numbered 1 to 88 from the bottom. MIDI uses a different count in which A4 is 69 and middle C is 60, so a MIDI note number is always the piano key number plus 20: the lowest piano key, A0, is MIDI 21 and the highest, C8, is MIDI 108.

How to calculate the frequency of a note

To calculate the frequency of a note, count how many semitones it lies above or below A4 and multiply 440 Hz by 2 raised to that number divided by 12. For piano key n the formula is f = 440 × 2^((n − 49)/12). Key 49 is A4, so the exponent is zero and the result is 440 Hz.

Worked example 1, middle C: C4 is key 40, nine semitones below A4. 2^(−9/12) = 0.5946, and 440 × 0.5946 = 261.63 Hz. Worked example 2, E4: key 44, five semitones below A4. 2^(−5/12) = 0.7492, and 440 × 0.7492 = 329.63 Hz. Worked example 3, A5: key 61, twelve semitones above. 2^(12/12) = 2, and 440 × 2 = 880 Hz, the octave.

The same formula works with MIDI numbers if you replace 49 with 69: f = 440 × 2^((m − 69)/12). To use another reference pitch, replace 440 with it. At A4 = 432 Hz, middle C becomes 432 × 0.5946 = 256.87 Hz.

Why 2^(1/12)? Twelve-tone equal temperament splits the octave, a doubling of frequency, into 12 equal steps. Twelve equal multiplications must give 2, so each step is the twelfth root of 2, about 1.05946. That is why every semitone is the same ratio while the gap in hertz grows as you go up: A4 to A♯4 is 26.16 Hz, but A0 to A♯0 is only 1.64 Hz.

Middle C frequency: 261.63 Hz

Middle C, C4, has a frequency of about 261.63 Hz at the standard A4 = 440 Hz. It is key 40 of 88, near the middle of the keyboard, and MIDI note 60. Its wavelength in air at 20 °C is about 1.3 metres.

You will sometimes see middle C given as 256 Hz. That is "scientific pitch", also called Sauveur pitch or "Verdi tuning", first proposed by Joseph Sauveur in 1713. It puts every C on a power of 2 (128, 256, 512 Hz), which is handy in science, and it is why medical tuning forks are often 128, 256 or 512 Hz. Orchestras do not use it. Middle C at 256 Hz is about 37.6 cents lower than at A440, and A then falls to about 430.54 Hz.

A4 = 432 Hz gives middle C at 256.87 Hz, close to 256 but not the same: 432 Hz tuning and scientific pitch are two different systems that people often mix up.

Hz to note: how to convert a frequency into a note

To convert a frequency into a note, find how many semitones it lies from A4: n = 49 + 12 × log2(f / 440). Round n to the nearest whole number to get the piano key; the leftover fraction times 100 is how many cents the frequency is sharp (+) or flat (−) of that note.

Worked example, 300 Hz: 300 / 440 = 0.6818; log2(0.6818) = −0.5525; times 12 gives −6.63; plus 49 gives 42.37. Key 42 is D4 (293.66 Hz), and 0.37 of a semitone is 37 cents, so 300 Hz is D4 + 37 cents. Worked example, 1,000 Hz: n = 63.21, which is B5 (987.77 Hz) + 21 cents.

If the fraction is close to 0.5, the frequency sits halfway between two notes, a quarter-tone off either. That is common for numbers chosen for reasons other than music, like round figures or frequencies sold as having special properties.

The frequencies in this table are the tuning forks offered on this site's tuning fork page, plus two round numbers. The C-based forks all land 37.6 cents below the equal-tempered C because they follow scientific pitch, not A440.

What are cents in music, and how many can you hear?

A cent is one hundredth of an equal-tempered semitone. An octave has 1,200 cents, and one cent is a frequency ratio of about 1.00058. Alexander J. Ellis defined the unit in the 1880s so that intervals could be compared without dealing with awkward ratios. The interval between any two frequencies in cents is 1200 × log2(f2 / f1); from 432 Hz to 440 Hz, for example, is 31.77 cents.

Cents are useful because they mean the same thing at every pitch. A difference of 3 Hz is about 47 cents at 110 Hz, 23 cents at 220 Hz and 12 cents at 440 Hz. Hertz tell you about the sound wave; cents tell you what the ear hears as an interval.

How small a difference can people notice? For sine tones, the smallest noticeable change is roughly 3 Hz below 500 Hz and about 0.6 % above 1,000 Hz, which is about 10 cents. The best-trained listeners near 1 kHz can do better than 0.1 %. These figures depend on how they are measured, so treat them as approximate.

Training makes a large difference. In a lab study of 30 classical musicians and 30 non-musicians (Micheyl and colleagues, 2006), the non-musicians' thresholds were at first more than six times larger than the musicians', still about four times larger after 2 hours of practice, and matched the musicians after 4–8 hours of training.

Piano frequency range: the lowest and highest notes

A standard 88-key piano runs from A0 at 27.5 Hz to C8 at about 4,186.01 Hz, a ratio of about 152 to 1. That is seven full octaves from A0 to A7 (3,520 Hz) plus three more semitones up to C8. The keyboard has 52 white keys and 36 black keys.

The numbers in a note chart are fundamentals, the lowest frequency of each note. A real piano string also sounds overtones above it, so a piano produces sound well above 4,186 Hz even though no key has a higher fundamental. A pure sine tone at the same frequency, which is what a tone generator plays, has no overtones at all and sounds plainer.

Compared with human hearing, the piano sits comfortably inside it. Hearing is commonly given as 20 to 20,000 Hz, and it is most sensitive between about 2,000 and 5,000 Hz. The lowest A has a wavelength in air of about 12.5 metres; the top C, about 8 cm. On phone and laptop speakers the bottom octave of the chart may be very weak or silent, so use headphones if you want to hear A0.

A440, A432 or A415: what the reference pitch changes

The reference pitch is the frequency chosen for A4, and every other note is calculated from it. ISO 16:1975 sets it at 440 Hz for the note A in the treble stave, to an accuracy of 0.5 Hz. The history runs from France fixing A = 435 Hz on 16 February 1859, through a London meeting of delegates from five countries agreeing on 440 Hz in May 1939, to ISO adopting it in 1955 and confirming it as ISO 16 in 1975.

Changing the reference moves every note by the same number of cents. At A4 = 432 Hz every note is 31.77 cents lower than at 440 Hz, about a third of a semitone: C4 becomes 256.87 Hz, E4 323.63 Hz, A0 27 Hz. The intervals between the notes stay exactly the same, so a melody keeps its shape and only sits slightly lower.

The chart above can also use A4 = 415 Hz. Whether 432 Hz sounds better than 440 Hz, what the studies found and where the claims about it come from is covered in detail on this site's page 432 Hz vs 440 Hz, so it is not repeated here.

Note names: C D E F G A B, H, and do re mi

The same piano key has different names in different countries, which causes real confusion when reading a chart. English uses the letters C D E F G A B. German and Lithuanian use the same letters with one important difference: the note English calls B is called H, and the letter B means B♭, one semitone lower. So a Lithuanian or German "B" is 466.16 Hz in the fourth octave, not 493.88 Hz.

Russian uses solfège syllables: до, ре, ми, фа, соль, ля, си. Here the syllable is fixed to the note, so до is always C and ля is always A, whatever the key of the music.

If a chart from another country seems to be off by a semitone on one note, check whether its B means your B or your B♭.

What note frequencies are useful for

A note chart is handy whenever sound is described in hertz and you want to know what it is musically, or the other way round. Some practical uses:

• Tuning by ear: play the target note from the chart and match your instrument to it.
• Reading a tuner or an analyser: a spectrum display shows a peak at, say, 196 Hz; the chart tells you that is G3.
• Setting synthesizers and test tones: a tone generator takes hertz, so the chart turns note names into numbers you can type in.
• Checking claims about "special" frequencies: convert the number to a note and see where it lands. 528 Hz, for example, is C5 plus about 16 cents in standard tuning.
• Ear training: play two neighbouring keys a semitone apart on the piano above, then try a 10- or 20-cent difference with the tone generator.

To hear a single frequency on its own, with a choice of waveform and an exact number box, use this site's tone generator. For a fading, fork-like tone at 440, 432, 256, 512, 128 or 528 Hz, use the tuning fork page.