Short answer
In equal temperament with A4 = 440 Hz, key *n* (1 to 88) sounds at 440 × 2^((n − 49) ÷ 12) Hz. The lowest key, A0, is 27.50 Hz; middle C (C4) is 261.63 Hz; the top key, C8, is 4,186.01 Hz.
A real piano is stretched away from these numbers: a little flat in the bass and sharp in the treble. The table shows a typical grand's stretch next to each key.
Key numbers count from the bottom (A0 = 1). Note names use scientific pitch notation, where middle C is C4. "Typical stretch" is how far a typical grand piano's tuning sits from the equal-tempered frequency, in cents (100 cents = one semitone).
| Key | Note | Frequency (Hz), A4 = 440 | Typical stretch (cents) |
|---|---|---|---|
| 88 | C8 | 4186.01 | +30 |
| 87 | B7 | 3951.07 | +28 |
| 86 | A♯7 | 3729.31 | +26 |
| 85 | A7 | 3520.00 | +24 |
| 84 | G♯7 | 3322.44 | +23 |
| 83 | G7 | 3135.96 | +21 |
| 82 | F♯7 | 2959.96 | +20 |
| 81 | F7 | 2793.83 | +19 |
| 80 | E7 | 2637.02 | +17 |
| 79 | D♯7 | 2489.02 | +16 |
| 78 | D7 | 2349.32 | +15 |
| 77 | C♯7 | 2217.46 | +14 |
| 76 | C7 | 2093.00 | +13 |
| 75 | B6 | 1975.53 | +12 |
| 74 | A♯6 | 1864.66 | +12 |
| 73 | A6 | 1760.00 | +11 |
| 72 | G♯6 | 1661.22 | +11 |
| 71 | G6 | 1567.98 | +10 |
| 70 | F♯6 | 1479.98 | +10 |
| 69 | F6 | 1396.91 | +9 |
| 68 | E6 | 1318.51 | +9 |
| 67 | D♯6 | 1244.51 | +8 |
| 66 | D6 | 1174.66 | +7 |
| 65 | C♯6 | 1108.73 | +7 |
| 64 | C6 | 1046.50 | +6 |
| 63 | B5 | 987.77 | +6 |
| 62 | A♯5 | 932.33 | +5 |
| 61 | A5 | 880.00 | +4 |
| 60 | G♯5 | 830.61 | +4 |
| 59 | G5 | 783.99 | +3 |
| 58 | F♯5 | 739.99 | +3 |
| 57 | F5 | 698.46 | +3 |
| 56 | E5 | 659.26 | +2 |
| 55 | D♯5 | 622.25 | +2 |
| 54 | D5 | 587.33 | +2 |
| 53 | C♯5 | 554.37 | +1 |
| 52 | C5 | 523.25 | +1 |
| 51 | B4 | 493.88 | +1 |
| 50 | A♯4 | 466.16 | +0 |
| 49 | A4 | 440.00 | +0 |
| 48 | G♯4 | 415.30 | -0 |
| 47 | G4 | 392.00 | -0 |
| 46 | F♯4 | 369.99 | -0 |
| 45 | F4 | 349.23 | -1 |
| 44 | E4 | 329.63 | -1 |
| 43 | D♯4 | 311.13 | -1 |
| 42 | D4 | 293.66 | -1 |
| 41 | C♯4 | 277.18 | -1 |
| 40 | C4 | 261.63 | -1 |
| 39 | B3 | 246.94 | -1 |
| 38 | A♯3 | 233.08 | -2 |
| 37 | A3 | 220.00 | -2 |
| 36 | G♯3 | 207.65 | -2 |
| 35 | G3 | 196.00 | -2 |
| 34 | F♯3 | 185.00 | -2 |
| 33 | F3 | 174.61 | -2 |
| 32 | E3 | 164.81 | -2 |
| 31 | D♯3 | 155.56 | -2 |
| 30 | D3 | 146.83 | -2 |
| 29 | C♯3 | 138.59 | -2 |
| 28 | C3 | 130.81 | -2 |
| 27 | B2 | 123.47 | -2 |
| 26 | A♯2 | 116.54 | -2 |
| 25 | A2 | 110.00 | -3 |
| 24 | G♯2 | 103.83 | -3 |
| 23 | G2 | 98.00 | -3 |
| 22 | F♯2 | 92.50 | -3 |
| 21 | F2 | 87.31 | -3 |
| 20 | E2 | 82.41 | -3 |
| 19 | D♯2 | 77.78 | -3 |
| 18 | D2 | 73.42 | -3 |
| 17 | C♯2 | 69.30 | -3 |
| 16 | C2 | 65.41 | -4 |
| 15 | B1 | 61.74 | -4 |
| 14 | A♯1 | 58.27 | -4 |
| 13 | A1 | 55.00 | -5 |
| 12 | G♯1 | 51.91 | -5 |
| 11 | G1 | 49.00 | -5 |
| 10 | F♯1 | 46.25 | -6 |
| 9 | F1 | 43.65 | -6 |
| 8 | E1 | 41.20 | -6 |
| 7 | D♯1 | 38.89 | -7 |
| 6 | D1 | 36.71 | -7 |
| 5 | C♯1 | 34.65 | -8 |
| 4 | C1 | 32.70 | -9 |
| 3 | B0 | 30.87 | -10 |
| 2 | A♯0 | 29.14 | -11 |
| 1 | A0 | 27.50 | -12 |
Frequencies from Pianowise's equal-temperament function. The stretch column is Pianowise's typical-grand model (standard octave style) before any notes are measured; your piano's real stretch depends on its strings and is what Pianowise measures.
Piano strings are stiff, so their overtones run sharp of exact multiples. Octaves tuned to sound clean come out slightly wider than 2:1, and across the keyboard the tuning stretches: flatter at the bottom, sharper at the top. In our measurements of a Yamaha C5 grand sample set, the bottom keys sat about −24 cents and the treble rose to about +20 cents by B6. See stretch tuning.
261.63 Hz in equal temperament with A4 = 440 Hz. Middle C is C4, key 40 of 88.
A0, the lowest key, is 27.50 Hz in equal temperament. Its fundamental is weak; you mostly hear its higher partials.
C8, the top key, is 4,186.01 Hz in equal temperament; a tuned piano usually sits a little sharper than that.
f(n) = 440 × 2^((n − 49) ÷ 12) for key n from 1 (A0) to 88 (C8).
A-440 is the international standard pitch; the Piano Technicians Guild notes that pianos are designed to sound their best tuned to it, and it lets a piano play with other instruments.
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