Guitar Fret Calculator

A fretted instrument divides a vibrating string into repeatable musical intervals. In twelve-tone equal temperament, each semitone raises frequency by the twelfth root of two. Because frequency is inversely proportional to vibrating string length, the remaining length at fret number n equals the open scale length divided by two raised to n divided by twelve. Subtracting that remaining length from the full scale gives the fret's measured position from the nut. The twelfth fret is the easiest checkpoint because it sits at exactly half the scale length and sounds one octave above the open string. On a 25.5-inch guitar scale, the twelfth fret is 12.75 inches from both nut and bridge. Earlier frets are farther apart; spacing narrows progressively toward the bridge. This geometric pattern is more accurate than repeatedly dividing the remaining length by the traditional rule-of-18 approximation. Scale length means the theoretical vibrating distance from the nut's witness point to the bridge saddle. It is not simply the physical length of the fretboard. Common electric guitar scales include 24.75 and 25.5 inches, while many bass guitars use 34 inches. Builders working metrically can enter the same dimension in millimeters because the formula preserves whichever unit is selected. The table reports cumulative distance from the nut and remaining theoretical distance to the bridge for every fret. For layout work, mark cumulative positions from one fixed datum rather than adding adjacent gaps; this prevents small measurement and rounding errors from accumulating. Retain more precision during layout than the displayed three decimal places when machining slots with computer-controlled equipment. Real instruments need compensation because pressing a string stretches it and raises its pitch slightly. Saddles are therefore normally placed beyond the nominal scale endpoint, with different offsets for different strings. Nut height, action, string gauge, material stiffness, and playing pressure also affect intonation. The mathematical fret positions remain based on the nominal scale, while setup adjustments happen at the nut and bridge. Use these results for planning, templates, repair checks, and educational comparisons, then follow established lutherie practices for slot width, crown position, compensation, and final intonation.