The 12th root of two
Fret calculator
Fret positions on a modern guitar are not even steps. Each fret is placed so the sounding length shortens by a factor of the twelfth root of two, which is one semitone. The distance from the nut to fret n is scale length times (1 − 2^(−n/12)). The gap from the previous fret is the difference of those two distances, and it gets smaller as n grows.
What to do with the table
Pick a preset that matches the guitar you are thinking about: 25.5 for many Fenders, 24.75 for many Gibsons, 25 for a common PRS-style length, 25.4 for a lot of Martins, 27 if you are in baritone territory. Add an open string if you also want the note and frequency at that fret. The frequencies assume A4 = 440 and equal temperament. They are the same targets the intonation tester listens for.
Ideal, not your neck
The table is the drawing, not a photo of the fingerboard. A nut that sits a little far, a fret that was leveled low, or a conversion neck will not match every row. Use the numbers to check a plan or to understand why the first fret gap is the widest. Do not sand anything because a row in a browser said so.
Questions
- Why is fret 12 at half the scale?
- Because twelve semitones is an octave, and an octave is half the sounding length. The nut-to-12th-fret distance is half the scale, so the remaining string is the other half.
- Can I enter millimetres?
- Yes. Switch the unit. The rule does not change; only the labels do.