Note Frequency Calculator

Enter how many semitones sit from A4. The calculator finds frequency with f = 440 × 2^(k/12). Zero is concert 440 Hz; plus 12 is A5 = 880 Hz; minus 12 is A3 = 220 Hz. Minus 9 is C4, about 261.63 Hz. The note name, octave, cents, and MIDI number come from the same semitone count. A 432 Hz reference is not in this formula.

Result

Enter semitones from A4. The result shows up here.

Interval from two Hz values: semitones between frequencies. A shift: transpose in Hz. Quotient: frequency quotient. Cents: cents to semitones. Wave: sound wavelength.

How it works

440 × 2^(−9/12) → 261.63 Hz

A4440 Hz

k−9

C4261.63 Hz

Equal temperament splits the octave into twelve even semitones. Each semitone multiplies frequency by the twelfth root of 2, about 1.05946. We start from A4 = 440 Hz, not 432. The formula is f = 440 × 2^(k/12). Entered 0 is A4 and returns 440.00 Hz.

Plus 12 is A5 = 880.00 Hz. Minus 12 is A3 = 220.00 Hz. Plus 3, three semitones above A, is C5 ≈ 523.25 Hz. Minus 9 is C4 ≈ 261.63 Hz. Plus 7 is E5 ≈ 659.26 Hz, a tempered fifth, not just 660. Plus 2 is 493.88 Hz. Minus 5 is E4 ≈ 329.63 Hz.

Negative k is allowed and means notes below A4. MIDI 69 is A4, so k = n − 69. MIDI 60 (C4) is −9, MIDI 72 (C5) is +3. There is no octave cap in the code, but extreme k quickly leaves the hearing range. The result has two decimal places in hertz.

Note hertz from A4 = 440 Hz in 12-TET. If the base should be something other than 440, open transposition and enter your own f1. If you already have two frequencies, the interval page gives you k, not hertz from concert pitch.

Enter k and click Calculate. A comma or a period in 0.5 (fifty cents above A4) works. Wavelength from those hertz is on the neighboring page: 440 Hz at 343 m/s is 0.7795 m.

On a score you count semitones from A first, then hertz. A tuner that only shows cents does not replace this formula: convert the cents separately and add them to k as a fraction.

The note name, octave, cents, and MIDI number are results from the same k. The calculator rounds k to the nearest semitone and names it in scientific pitch. At k = −9 the name is C4, the octave is 4, and the offset is 0 cents. At k = 0.5 the frequency is 452.89 Hz, the nearest note is A♯4 / B♭4, and the offset is −50 cents. The drawing runs from C of that octave to the next C, and equal gaps are equal semitones. Wavelength, transposition from another concert pitch, the quotient of two frequencies, and cents as their own input are on neighboring pages.

How to use

Enter the semitone offset from A4. Zero is A4 = 440 Hz. Negative values go down.
For C4 enter −9, for C5 enter 3, for A5 enter 12. The buttons fill the same field. A 432 Hz concert pitch is not in this formula.
Click Calculate. 0 gives 440.00 Hz, 12 gives 880.00 Hz, and −12 gives 220.00 Hz.
The note name, octave, cents, and MIDI number appear from the same k. At −9 that is C4, octave 4, and 0 cents.
When the base is not 440, open transposition and enter your own f1 plus the same k. For a wave from these hertz, open sound wavelength. For k from two Hz values, open the interval page.

Formula

f = 440 × 2^k/12

nearest semitone = rounding k to a whole number

cents = (k − nearest semitone) × 100

The symbol k means semitones from A4. A4 = 440 Hz in ISO 16 and in equal temperament. Negative k is allowed. An empty field is not zero until you enter a number. The hertz result shows two decimal places.

The name and octave come from the MIDI number of the nearest semitone, which is 69 + k after rounding. On an exact halfway step the calculator chooses the higher semitone. At k = 0.5 the nearest note is A♯4 / B♭4, and the cents are −50.

The formula has no single author. It is the standard equal-tempered spelling from concert A4. The calculator does not change the 440 Hz base. It does not compute wavelength, the quotient of two frequencies, or transposition from another concert pitch.

Note Hz from A4 = 440

Here f = 440 × 2^(k/12). Zero semitones is 440 Hz. Plus 12 is A5 = 880 Hz, minus 12 is A3 = 220 Hz. Minus 9 is C4, 261.63 Hz.

Hz: Hertz of the result, cycles per second. A4 in this calculator is 440. k = 3 gives C5 = 523.25 Hz. Empty k is not a concert-pitch zero.
A4: Concert pitch, the 440 Hz base at k = 0. ISO 16 takes this pitch. Every other note is 2^(k/12) from that 440 Hz, in equal temperament.
k: Semitones from A4. Zero is A4. Plus 12 is one octave up. Minus 9 is C4. A fraction, for example 0.5, leaves the note between semitones.
note: Name of the nearest semitone in scientific pitch. At k = 2 that is B4. At k = 0.5 that is A♯4 / B♭4. This is the same tuning, not a second system.
octave: The octave number of that note. C4 is octave 4. A4 is octave 4. A5 is octave 5. This is not a wavelength.
cents: Offset from the nearest note. One hundred cents make one semitone. At k = 0 the cents are 0. At k = 0.5 they are −50, because the nearest higher semitone is A♯4 / B♭4.

Real-life examples

Example 1

Zero semitones gives 440.00 Hz. That is A4 in octave 4, at 0 cents. The MIDI number is 69.

Example 2

Plus 12 gives 880.00 Hz. That is A5 in octave 5, at 0 cents.

Example 3

Minus 12 gives 220.00 Hz. That is A3 in octave 3, at 0 cents.

Example 4

Plus 3 gives 523.25 Hz. That is C5 in octave 5, at 0 cents.

Example 5

Minus 9 gives 261.63 Hz. That is C4 in octave 4, at 0 cents.

Example 6

Plus 7 gives 659.26 Hz. That is E5, a tempered fifth from A4, at 0 cents.

Example 7

Plus 2 gives 493.88 Hz. In scientific pitch that is B4.

Example 8

Minus 5 gives 329.63 Hz. That is E4, five semitones below A4.

Example 9

Half a semitone, 0.5, gives 452.89 Hz. The nearest note is A♯4 / B♭4, and the offset is −50 cents.

Ways to use this calculator

You check how many Hz a MIDI note has after counting semitones from A4, before you set an oscillator.
You compare concert 440 with a scored note when the tuner only shows a cents offset.
You take k = 7 and confirm 659.26 Hz before someone hands you just 660 as a pure fifth.
You read that k = −9 is C4 at 261.63 Hz before you set an oscillator.

Frequently asked questions

How many Hz are A4, A5, and A3?

440.00 Hz, 880.00 Hz, and 220.00 Hz. Zero, plus 12, and minus 12 semitones from A4. Those notes are A4, A5, and A3, in octaves 4, 5, and 3, at 0 cents.

What k do I enter for C4 and C5?

C4 is −9, which is 261.63 Hz in octave 4. C5 is +3, which is 523.25 Hz in octave 5. The offset is 0 cents.

How many Hz is a fifth from A4?

659.26 Hz at k = 7. That note is E5. Just 3:2 would be 660 Hz. This page is 12-TET.

What is the result at k = 2 and k = −5?

493.88 Hz and 329.63 Hz. The second is E4, five semitones below A4. The first is B4.

Is entered 0 really 440 Hz?

Yes. 440 × 2^0 = 440. That is concert A4, not missing data. The octave is 4, and the offset is 0 cents.

How do I turn a MIDI number into k?

Subtract 69. MIDI 69 is A4. MIDI 60 is C4 and k = −9. MIDI 72 is C5 and k = 3. The result shows the nearest MIDI number of that same note.

Can I compute from 432 Hz?

Not in this calculator. The base is 440. For 432, open transposition and enter f1 = 432.

Can k be a fraction?

Yes. 0.5 is fifty cents above A4 and 452.89 Hz. The nearest note is A♯4 / B♭4, and the offset from it is −50 cents. On an exact halfway step the calculator chooses the higher semitone.

Where do I take wavelength from these hertz?

On the sound-wavelength page. 440 Hz and 343 m/s give 0.7795 m.

How is this different from transposition?

Here the base is always 440. There you enter your own f1 and the same k. A quotient of two hertz values, and cents as their own input, live on separate pages.

Where do the note name and octave come from?

They come from the same k. The nearest MIDI number is 69 plus k rounded to a whole semitone. The remainder after division by 12 is the name, and the octave is the integer part of that number minus 1. At k = −9 the name is C4. A sharp and a flat are two names for one semitone, not a second pitch system.

How do I calculate a note frequency in hertz?

Use f = 440 × 2^(k/12), where k is semitones from A4. At k = 0: 440 Hz. At k = −9: 440 × 2^(−9/12) ≈ 261.63 Hz (C4).

How many Hz is middle C (C4) at A4 = 440 Hz?

About 261.63 Hz. Enter k = −9, because MIDI 60 is nine semitones below MIDI 69 (A4).

How do I get frequency from a MIDI number on this page?

Compute k = n − 69 and enter k. MIDI 69 is A4 = 440 Hz. MIDI 60 (C4) is −9 ≈ 261.63 Hz. MIDI 72 (C5) is +3 ≈ 523.25 Hz.

How does 12-TET differ from a pure 3:2 fifth?

At k = 7 the calculator gives E5 ≈ 659.26 Hz. A pure 3:2 fifth from 440 Hz is 660 Hz. The gap is equal temperament, not rounding error.

Why is there no A4 = 432 Hz field?

The page formula is anchored at 440 Hz. Another reference with the same semitone shift belongs on the frequency transposition calculator.

How many Hz is guitar high E (E4) at A4 = 440?

E4 is k = −5: 440 × 2^(−5/12) ≈ 329.63 Hz. That is 12-TET, not a separate guitar tuner preset.

Updated November 3, 2026 · Hubert Ligocki

At k = −9 the result is 261.63 Hz. That is C4, octave 4, 0 cents.

Knowledge sources

Frequency and intervals in this calculator follow the hertz, A440 concert pitch from ISO 16, and equal temperament.

Page updated November 3, 2026.