Note frequency calculator and chart

Turn a frequency into a note and a cents offset, or a note into its frequency, at whatever pitch A4 is tuned to. The full chart below follows the same setting.

445 Hz is closest to

A4 +19.6¢

A4 is 440.00 Hz at A4 = 440 Hz, so 445 Hz is 19.6 cents sharp. C4 is 261.63 Hz (MIDI 60).

Frequency of every note, C0 to B8, at A4 = 440 Hz

Rows are notes, columns are octaves in scientific pitch notation. A standard 88-key piano runs from A0 to C8.

Note	Octave 0	Octave 1	Octave 2	Octave 3	Octave 4	Octave 5	Octave 6	Octave 7	Octave 8
C	16.352	32.703	65.406	130.81	261.63	523.25	1046.5	2093.0	4186.0
C#	17.324	34.648	69.296	138.59	277.18	554.37	1108.7	2217.5	4434.9
D	18.354	36.708	73.416	146.83	293.66	587.33	1174.7	2349.3	4698.6
D#	19.445	38.891	77.782	155.56	311.13	622.25	1244.5	2489.0	4978.0
E	20.602	41.203	82.407	164.81	329.63	659.26	1318.5	2637.0	5274.0
F	21.827	43.654	87.307	174.61	349.23	698.46	1396.9	2793.8	5587.7
F#	23.125	46.249	92.499	185.00	369.99	739.99	1480.0	2960.0	5919.9
G	24.500	48.999	97.999	196.00	392.00	783.99	1568.0	3136.0	6271.9
G#	25.957	51.913	103.83	207.65	415.30	830.61	1661.2	3322.4	6644.9
A	27.500	55.000	110.00	220.00	440.00	880.00	1760.0	3520.0	7040.0
A#	29.135	58.270	116.54	233.08	466.16	932.33	1864.7	3729.3	7458.6
B	30.868	61.735	123.47	246.94	493.88	987.77	1975.5	3951.1	7902.1

Open strings of common instruments

Instrument	Strings, low to high as usually listed
Guitar, standard tuning	E2 82.407 HzA2 110.00 HzD3 146.83 HzG3 196.00 HzB3 246.94 HzE4 329.63 Hz
Bass guitar, 4-string	E1 41.203 HzA1 55.000 HzD2 73.416 HzG2 97.999 Hz
Violin	G3 196.00 HzD4 293.66 HzA4 440.00 HzE5 659.26 Hz
Cello	C2 65.406 HzG2 97.999 HzD3 146.83 HzA3 220.00 Hz
Ukulele, standard (re-entrant)	G4 392.00 HzC4 261.63 HzE4 329.63 HzA4 440.00 Hz

How to use it

Leave A4 at 440 Hz unless you are working to a different reference. Type a frequency into the middle field to see the nearest note and how far it is from that note in cents: a positive number is sharp, a negative one flat. Type a note name into the right-hand field to read its exact frequency and MIDI number. Sharps are written with # and flats with b, and octave numbers can go below zero, as in C-1 (MIDI 0).

The formula

In twelve-tone equal temperament every semitone multiplies the frequency by the same ratio, the twelfth root of two (about 1.05946), so twelve of them make exactly one octave, a doubling. Numbering notes the MIDI way, with A4 as note 69:

f = A4 × 2^{(n − 69) / 12}
n = 69 + 12 × log2(f / A4), rounded to the nearest whole note
cents = 1200 × log2(f / f_note)
wavelength = 343 / f metres in air at 20 °C

Worked example. 445 Hz gives n = 69 + 12 × log2(445 / 440) = 69.196, which rounds to 69, A4. The offset is 1200 × log2(445 / 440) = +19.6 cents. Middle C is 440 × 2^{(60 − 69)/12} = 440 × 2^−0.75 = 261.63 Hz. Retune to A4 = 432 Hz and the same C becomes 256.87 Hz.

Octave numbers follow scientific pitch notation, in which each octave starts on C: B3 is followed by C4. This is why the chart runs C to B rather than A to G#.

Where it stops being reliable

The numbers are exact for equal temperament, but real instruments are not always tuned that way. Pianos are deliberately stretch-tuned: because their strings are stiff, their overtones run sharp, and tuners push the top octaves sharp and the bottom octaves flat, often by 10 to 30 cents at the extremes, so the instrument sounds in tune with itself. A piano measured against this chart will look out of tune at both ends when it is not.

Choirs, string quartets and brass sections often drift towards just intonation in sustained chords, where a major third is about 14 cents narrower than the equal-tempered one. And a single frequency reading from a tuner or analyser is only as good as its detection of the fundamental; low notes on small speakers are often heard through their harmonics alone.

To hear any frequency, play it on the tone generator.

Common questions

5 answers

What frequency is middle C?

Middle C is C4, 261.63 Hz when A4 is tuned to 440 Hz. It is MIDI note 60. Some manufacturers, notably Yamaha, label middle C as C3 in their software and keyboards, so the same key can carry two names; the frequency does not change.

What is a cent?

One hundredth of an equal-tempered semitone, so an octave is 1200 cents. Because it is a ratio, a cent is a smaller step in hertz at low pitches than at high ones: about 0.03 Hz at A1 (55 Hz) but about 1 Hz at A6 (1760 Hz). Most listeners can hear a difference of around 5 to 10 cents between two tones played one after the other, less when they sound together and beat against each other.

Why tune to A = 440 Hz?

It is the international standard pitch, set out in ISO 16. Before standardisation, reference pitches varied widely between cities and eras. Many orchestras today tune slightly higher, often 442 or 443 Hz, and baroque ensembles commonly use 415 Hz, roughly a semitone below modern pitch. Set the A4 field to any of these and the chart follows.

Is 432 Hz tuning better?

It is a different reference pitch, about 31.8 cents (a third of a semitone) below 440. Claims that it is more natural, more in tune with the body or healing are not supported by scientific evidence. If you like how your instrument sounds there, it is a perfectly usable tuning, and the chart will show every note at A4 = 432.

Does this chart work for other tuning systems?

No. It is twelve-tone equal temperament only, where every semitone is the same ratio. Just intonation, Pythagorean tuning, meantone and the stretched tuning used on real pianos all place some notes several cents away from these values. For those you need a tuner or table built for that system.

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