Fret Calculator (guitar fret positions from scale length, 12-TET)

Understanding the guitar fret position calculator — concept and principle

This calculator gives the distance from the nut to any fret on a fretted instrument, the gap between neighbouring frets and the position of the last fret, from the scale length. Luthiers, repairers and students use it to slot a fingerboard, check a neck, or design a custom instrument.

Fret position from the nut: with the default inputs the result is 324 mm (half the scale length).

How it is calculated

Distance from the nut to fret n: d = L × (1 − 2^(−n/12))

L is the scale length (inches are converted with 1 in = 25.4 mm).
Fret to bridge saddle = L − d.
Gap from the previous fret = d(n) − d(n − 1).
Fret 12 sits at L ÷ 2; fret 24 at ¾ L.

The principle

In twelve-tone equal temperament every fret raises the pitch by one semitone, a frequency ratio of 2^(1/12). A string's frequency is inversely proportional to its vibrating length (Mersenne's laws), so each fret must leave 2^(−1/12) ≈ 0.9439 of the length that was vibrating before. After n frets the remaining length is L × 2^(−n/12), and the fret sits at the difference from the full scale. Twelve frets halve the length, which doubles the frequency: one octave. Because the factor is constant, the gaps shrink steadily up the neck.

Worked example

Default inputs: scale length 648 mm, locate fret 12, 22 frets in total.

d(12) = 648 × (1 − 2^(−1)) = 648 × 0.5 = 324 mm = 12.756 in.
Fret to saddle = 648 − 324 = 324 mm.
d(11) = 648 × (1 − 2^(−11/12)) = 304.73 mm, so the gap = 19.27 mm.
Last fret (22) = 648 × (1 − 2^(−22/12)) = 466.2 mm.
Scale length used = 648 mm.

Each point is the calculator re-run with only “Scale length” changed; the gold point is the default example. Change the inputs above and this chart follows your numbers.

Scale length	Fret distance from the nut (mm)
162	81
324	162
486	243
648	324
810	405
972	486
1,296	648

How to read the result

Measure all fret positions from the nut, not from one fret to the next, so small errors do not add up. Fret slots are cut at these positions; the bridge saddle is then set a few millimetres beyond the scale length to compensate for the string stretching when pressed, which is handled at the bridge, not by moving frets. A 648 mm scale is typical of many classical and steel-string guitars.

Common mistakes

Using the old "rule of 18" (17.817) approximation instead of the exact formula.
Measuring from fret to fret and accumulating errors.
Entering the total guitar length instead of the scale length (nut to saddle).
Moving frets to fix intonation instead of adjusting the saddle.

Keep in mind: Slot cutting needs accurate tools and a reliable reference. Check positions against a known template before cutting an expensive fingerboard.

Frequently asked questions

Where is the 12th fret on a guitar?

Exactly halfway along the scale length; on a 648 mm scale it is 324 mm from the nut.

Why do frets get closer together?

Each fret removes the same fraction of the remaining string length, so the absolute gaps shrink.

What is the rule of 18?

An old approximation that divides the remaining length by about 17.817 for each fret; the exponential formula is exact.

Sources: Physics of strings: frequency inversely proportional to vibrating length (Mersenne's laws), e.g. H. F. Olson, Music, Physics and Engineering (Dover, 1967) · NIST Special Publication 811 (2008), Appendix B (1 in = 25.4 mm)

Checked 9 Nov 2026. Twelve-tone equal temperament (semitone ratio 2^(1/12)) with string frequency inversely proportional to vibrating length (Mersenne’s laws) — standard physics of strings; 1 in = 25.4 mm exactly.

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