Example 1
440 Hz and +12 -> 880.00 Hz.
New Hz after transposition calculator
Type a base frequency and how many semitones to move. The calculator multiplies f1 by 2 to the power k/12. 440 Hz plus 12 is 880 Hz, plus 7 is about 659.26 Hz. Minus 12 drops to 220 Hz.
Start from A4: note frequency. Interval backward: semitones from a Hz pair. Cents: cents to semitones.
Result
Enter a value. The result shows up here.
How it works
In equal temperament each semitone multiplies frequency by the twelfth root of 2, about 1.05946. That is f2 = f1 × 2^(k/12). From concert 440 Hz, plus 12 semitones (an octave) is exactly 880 Hz. Plus 1 is about 466.16 Hz. Plus 7, a tempered fifth, is about 659.26 Hz, not 660.
The base does not have to be A4. If you start from C4 typed as 261.63 Hz and add 12, the result is 523.26 Hz. Exact C5 from A4 plus 3 semitones is 523.25 Hz; the gap is the 261.63 rounding. You can also take an analyzer peak or an oscillator that is not sitting on 440.
k may be negative or fractional. Minus 12 halves the base. 0.5 is fifty cents up. Typed zero leaves f1 alone, because 2^0 = 1. The base frequency must be positive: zero hertz is not a tone.
In the form, hertz first, then k. A comma and a period are the same, so 261.63 and 261,63 are one base. The result has two decimal places, matching the cards on the page.
If you always start from A4 = 440 Hz, the note-frequency page is shorter: you do not type a base there. Here the base is yours. When you already have two frequencies and need k first, open the semitone interval page and paste the result here.
New hertz after a 12-TET shift. 3:2 from 440 would be 660 Hz. Here the 12-TET grid rules, the same one as on a typical MIDI keyboard.
How to use
- Type the base frequency in hertz, for example 440, or 261.63 if you start from C4.
- Type k in semitones. Plus goes up, minus goes down. Zero leaves the base. 0.5 is half a semitone.
- Click Calculate. 440 and 12 give 880.00 Hz. 440 and 7 give 659.26 Hz.
- If you only have two frequencies, find k on the interval page first, then come back.
- When the base should always be 440 Hz, open note frequency. There you type k alone.
Formula
f2 = f1 × 2k/12
f1 > 0. k may be negative or fractional. Typed k = 0 returns f1. Empty k is not zero.
New Hz after k semitones
Here f2 = f1 × 2^(k/12). 440 Hz plus 12 is 880 Hz, plus 7 is about 659.26 Hz. Minus 12 drops to 220 Hz. Typed k = 0 returns f1.
- Hz
- Base f1 and new f2 in hertz. 440 at k = 12 gives 880. At k = 7 about 659.26. f1 must be positive.
- semitones
- The shift k, which may be negative or fractional. Plus 12 is an octave up. Empty k is not zero; typed 0 leaves 440.
Real-life examples
Example 2
440 Hz and -12 -> 220.00 Hz.
Example 3
440 Hz and +7 -> 659.26 Hz.
Example 4
440 Hz and +1 -> 466.16 Hz.
Example 5
440 Hz and -1 -> 415.30 Hz.
Example 6
440 Hz and +5 -> 587.33 Hz.
Example 7
440 Hz and +24 -> 1760.00 Hz.
Example 8
261.63 Hz and +12 -> 523.26 Hz.
Ways to use this calculator
- You shift an oscillator by a known k when the base is not concert 440 Hz.
- You check the new Hz after a key change before you tune a second synth to the first.
- You add 50 cents (k = 0.5) to an analyzer peak and check the new frequency.
Frequently asked questions
How many Hz from 440 at plus 12, plus 7, and plus 1?
880.00 Hz, 659.26 Hz, and 466.16 Hz. Minus 12 is 220.00 Hz, minus 1 is 415.30 Hz.
How is this different from note frequency from A4?
There the base is always 440 Hz. Here you type your own f1, for example C4 or an analyzer peak.
Why is plus 7 from 440 Hz 659.26, not 660?
660 Hz would be a just fifth 3:2. This page is 12-TET: 440 × 2^(7/12). The gap is about 2 cents.
Can k be a fraction, for example −0.5?
Yes. Minus half a semitone is 50 cents down. The formula takes any finite k.
What does typed zero in the semitone field do?
It returns the base unchanged, because 2^0 = 1. That is a deliberate shift of zero, not missing data.
What do I get from 261.63 Hz plus 12?
523.26 Hz. Exact C5 from A4 plus 3 is 523.25 Hz; 261.63 is already rounded.
Is plus 24 from 440 really 1760 Hz?
Yes. Every 12 semitones doubles. 440 × 4 = 1760. Two octaves up.
How do I turn tuner cents into k?
Divide cents by 100 on the cents page. 14 cents is k = 0.14, then paste it here.
Can f1 sit below 20 Hz?
The formula does not lock the hearing range. You get mathematical Hz. Whether a speaker plays it is another question.
Does a comma in 261.63 or 1.5 work?
Yes. A comma and a period are the same number. Avoid spaces inside the digits.
Knowledge sources
Frequency and intervals in this calculator follow the hertz and A440 concert pitch.
Page updated in 2026.