Fret Calculator

How Fret Positions Are Calculated

Every fret's distance from the nut follows one formula, derived from 12-tone equal temperament — the same tuning system behind note frequencies. Each fret shortens the vibrating string length by a fixed ratio, the 12th root of 2, so that 12 frets (one octave) together cut the string exactly in half:

$$d_N = L \times \left(1 - \frac{1}{2^{N/12}}\right)$$

This is the standard formula used by luthiers and fret-slot calculators worldwide. It comes directly from equal temperament: each semitone raises pitch by a factor of the 12th root of 2 (about 1.05946), and pitch on a vibrating string is inversely proportional to length — so each fret must shorten the remaining string length by that same ratio to raise the pitch by exactly one semitone.

Worked Example: Fret 12 Is Always Exactly Half

Set N = 12 in the formula: $d_{12} = L \times (1 - 1/2^{12/12}) = L \times (1 - 1/2) = L \times 0.5$. This isn't an approximation — it holds exactly for any scale length, because fret 12 is one full octave above the open string, and an octave is by definition half the string length. It's the standard sanity check luthiers use when slotting a fretboard: measure to the halfway point of the scale length, and that should land exactly on fret 12.

Worked Example: A 25.5-Inch Scale Length

For a Fender-style 25.5-inch scale length, fret 1 sits about 1.431 inches from the nut, fret 12 sits at exactly 12.75 inches (half of 25.5), and fret 24 sits about 19.125 inches from the nut — each fret's spacing from the previous one shrinks steadily as you move up the neck, because the same proportional cut is being taken from an ever-shorter remaining length.

Fret Terms You Should Know

Scale length — the length of a string's vibrating portion, measured from the nut to the bridge saddle; it's the single input that determines every fret position.

Fret slot — the physical groove cut into the fretboard where a fret wire is seated, positioned at the calculated distance from the nut.

Compensation — a small adjustment luthiers make to bridge saddle positions beyond this formula's raw math, to correct for string stiffness and intonation drift in practice.

Multi-scale (fanned-fret) — a guitar design using two different scale lengths across the neck (longer on the bass side, shorter on the treble side), producing frets that aren't perpendicular to the strings. This calculator assumes a single, standard scale length.

Common Fret Calculation Mistakes

Measuring from the wrong reference point — every distance here is from the nut, not from the previous fret, unless it's specifically the "spacing from previous fret" column. Another common error: using the wrong scale length for the instrument, since bass guitars, mandolins, and ukuleles all use different standard scale lengths than a 6-string guitar, and mixing them up throws off every fret position by the same proportional amount.