Transpose Key Calculator

Work out transpose key instantly with clear inputs, formula shown and shareable results.

About Transpose Key Calculator

Transposition adds the semitone shift to the key's position in the twelve-note chromatic circle, wrapping around, and the frequency ratio is two to the power of semitones over twelve. Since an octave is twelve semitones, moving up three semitones raises every frequency by about 19%, which is exactly what makes a capo work.

Formulas

New key

new position = (original position + semitones) mod 12

Frequency ratio

ratio = 2 ^ (semitones / 12)

Worked example

With the default values below, Transpose Key Calculator returns New key of D#. Change any input above and every figure here is recalculated in your browser.

Inputs used

Original keyone of C, C#, D, D#, E, F, F#, G, G#, A, A#, B: C
Semitones to moveaccepts -24–24: 3

Results

New key: D#
Movement: Up 3 semitones
Interval moved: minor 3rd
Frequency ratio: 1.18921

Step by step

1Values used
2New key
3Frequency ratio
4New key= D#
5Movement= Up 3 semitones
6Interval moved= minor 3rd
7Frequency ratio= 1.18921

Assumptions and limits

The result is derived only from the 2 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
Figures are rounded for display to 5 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

How is the Transpose Key figure worked out?

new position = (original position + semitones) mod 12. Transposition adds the semitone shift to the key's position in the twelve-note chromatic circle, wrapping around, and the frequency ratio is two to the power of semitones over twelve.

Why does this matter?

Since an octave is twelve semitones, moving up three semitones raises every frequency by about 19%, which is exactly what makes a capo work.

What do I need to enter?

Enter original key, semitones to move. The defaults shown are a realistic worked example — swap in your own figures to get a result you can use.