Piano Key Frequency Calculator
Find the frequency of any piano key in equal temperament.
Look up all 88 keys from A0 to C8, convert between MIDI note numbers and frequencies, and explore alternative tuning systems.
Equal Temperament Modern pianos use 12-tone equal temperament (12-TET): the octave is divided into 12 equal semitones. Each semitone ratio = 2^(1/12) ≈ 1.05946. The frequency doubles with each octave. Standard concert pitch: A4 = 440 Hz (adopted as international standard in 1939, London).
The Formula f(n) = 440 × 2^((n−49)/12) Where n = key number on the piano (A0 = key 1, C8 = key 88, A4 = key 49). Or equivalently: f = A4_Hz × 2^(semitones_from_A4 / 12)
MIDI Note Numbers MIDI (Musical Instrument Digital Interface) uses numbers 0–127 for notes. Middle C (C4) = MIDI 60. A4 (440 Hz) = MIDI 69. Formula: f(MIDI) = 440 × 2^((MIDI − 69)/12) MIDI was developed in 1983 as a universal standard connecting synthesizers and computers.
Historical Tuning Systems Before equal temperament, many systems existed: Just intonation: pure frequency ratios (3/2 = perfect fifth, 5/4 = major third). Sounds pure but only in one key. Meantone temperament: compromise for keyboard instruments, common 1550–1800 Europe. Well temperament: Bach’s “Well-Tempered Clavier” (Germany, 1722) may have used a form of this. Today’s equal temperament allows playing in any key equally — at the cost of slight “impurity” in all intervals.
The Physics of Piano Strings String frequency: f = (1/2L) × √(T/μ) L = string length, T = tension, μ = mass per unit length. Higher notes: shorter, thinner strings. Lower notes: longer, heavier strings (wound with copper). Piano tuning is also affected by “inharmonicity” — real strings vibrate slightly sharper at harmonics than ideal strings, so pianos are stretched-tuned.
Concert A Variations A4 = 440 Hz: current international standard (ISO 16). A4 = 432 Hz: popular alternative in some alternative music communities (no scientific advantage). A4 = 415 Hz: Baroque pitch (commonly used for period instrument recordings). A4 = 466 Hz: High Baroque (some German orchestras in 1700s). A4 = 443–444 Hz: used by some European orchestras (Berlin Philharmonic, Vienna Philharmonic) for brighter sound.