Note Frequency Converter
Convert between a note name or MIDI note number and its frequency in Hz in 12-tone equal temperament. From a frequency, it also gives the nearest note and how far off it is, in cents.
The formula (12-tone equal temperament)
- Frequency = reference frequency × 2^((n − 69) ÷ 12), where n is the MIDI note number (A4 = 69). The reference frequency of A4 is 440 Hz by default.
- Conversely, n = 69 + 12 × log2(frequency ÷ reference frequency). The n found is rounded to the nearest whole number (the note), and the distance from it is given in cents.
- One cent is 1/100 of a semitone (an octave is 1,200 cents).
This is the definition of 12-tone equal temperament, not a clause of a standard. A4 = 440 Hz is the usual standard pitch. Other references such as 415, 432, 442 and 443 Hz are also used, which is why the reference frequency can be changed.
Octave numbers differ between systems
MIDI numbers the notes, and the name of the octave that goes with a number is a matter of convention. Two systems are in common use:
- C4 = MIDI 60 (the standard, scientific pitch notation): middle C is C4 and A4 = 440 Hz = MIDI 69.
- C3 = MIDI 60 (Yamaha style and some others): the same note is written one octave number lower (A3 = 440 Hz).
The pitch (the frequency) is the same either way; only the numbering differs. The switch changes how note names are shown and read by one octave. The result also shows the name in the other system for reference.
Examples (reference A4 = 440 Hz, C4 = MIDI 60 numbering)
- A4 = 440 Hz (MIDI 69). A3 = 220 Hz and A5 = 880 Hz.
- C4 (middle C) = about 261.63 Hz (MIDI 60).
- E4 = about 329.63 Hz.
- A0 = 27.5 Hz (MIDI 21, the lowest piano key) and C8 = about 4,186.01 Hz (MIDI 108, the highest piano key).
- With the reference at 442 Hz: A4 = 442 Hz and A3 = 221 Hz.
- 450 Hz is about +38.9 cents above A4 (440 Hz); the nearest note is A4.
- 432 Hz is about −31.8 cents below A4.
Finding the note from a frequency
- The nearest note is the one whose offset is from −50 cents up to (but not including) +50 cents. Exactly 50 cents goes to the higher note.
- The range is MIDI 0 (C-1) to 127 (G9): about 8.18 Hz to about 12,543.85 Hz with a reference of 440 Hz. Outside it, the tool tells you why there is no note.
- The offset in cents is measured from the nearest note's frequency. The interval between two arbitrary frequencies is not handled here.
Precision
The twelfth root of 2 is irrational, so the tool uses ordinary floating-point arithmetic, trims the result to 12 significant digits and rounds it to the number of decimal places you choose. The reference note and its octaves (A3, A5 and so on) are exact and use no floating point. You can show 0 to 4 decimal places.
Notes
- Enter a note as a letter C to B, an optional sharp or flat (#, ♯, b or ♭) and an octave number, such as A4, C#4 or Db3. Lower case is also read.
- The reference can be 390 to 500 Hz. The frequency to convert can be up to 6 digits before the decimal point and 6 decimal places.
- The pitch of a real instrument, or a tuner reading, can differ with the reference setting and the way it is measured.
Sources
- MIDI Association forum, "MIDI Octave and Note Numbering Standard": https://midi.org/community/midi-specifications/midi-octave-and-note-numbering-standard . Read on 2026-11-01. It is a community discussion thread, not the MIDI specification, and it shows that two octave-naming conventions (middle C as C3 and as C4) are in use for MIDI note 60.
- ISO 16, "Acoustics — Standard tuning frequency (Standard musical pitch)", which sets A4 = 440 Hz. The ISO page could not be read on 2026-11-01, so this was not re-checked in this version of the page. The statement is carried over from the earlier checking of the Japanese version of this tool.
Frequently asked questions
What does A4 = 440 Hz mean?
It means the A above middle C vibrates 440 times per second. It is the usual reference for tuning.
Is middle C C3 or C4?
It depends on the system. In scientific pitch notation it is C4, and in Yamaha style it is C3. The MIDI note number is 60 in both.
Why do some people tune to 442 Hz or 432 Hz?
Orchestras, instruments and eras use different reference pitches. This tool lets you change the reference frequency and see the resulting frequencies.