Music Performance
Calculate distance from nut to any fret on a fretted instrument.
Useful for guitar building and setup.
The fret position calculator computes the exact physical location of any fret on a guitar or other fretted instrument using the standard 12-tone equal temperament (12-TET) formula. Unlike the 17.817 calculator which uses an iterative method, this calculator applies the direct mathematical formula: Distance = Scale Length × (1 - 2^(-fret/12)). This approach is widely used by luthiers, repair technicians, and DIY builders to determine where each fret should be positioned on a fretboard. The calculator also provides the spacing between consecutive frets and the remaining distance to the bridge, giving builders comprehensive data for accurate instrument construction. Understanding fret positioning is fundamental to luthier work, as incorrect placement causes intonation problems and playability issues.
The calculator applies the 12-TET formula directly: the distance from the nut equals the scale length multiplied by (1 - 2^(-fret/12)). The power function (2^(-fret/12)) represents how the octave (frequency doubling) is divided into 12 equal semitones. For the spacing between frets, it calculates the previous fret's position using the same formula with (fret - 1) and subtracts it from the current fret position. This gives builders the incremental spacing needed between each fret slot.
Distance from Nut = Scale Length × (1 - 2^(-n/12)), where n is the fret number. Fret Spacing = Distance(n) - Distance(n-1). Remaining Length = Scale Length - Distance from Nut. The exponent (-n/12) divides the octave into equal logarithmic intervals.
Both use the same mathematical principle (12-TET equal temperament) but apply it differently. The 17.817 calculator uses an iterative algorithm that successively divides remaining length, while this calculator applies a direct closed-form formula. The results are mathematically equivalent, but this direct formula is more straightforward and commonly used in modern luthier software.
The formula (1 - 2^(-n/12)) represents the fractional position of a fret as a logarithmic function of frequency. The base-2 exponent reflects how frequency doubling (octaves) are divided: 2^(n/12) gives the frequency ratio for fret n relative to the open string. This logarithmic relationship ensures equal-sounding semitone intervals.
Yes, this calculator is completely agnostic to the number of strings. It only cares about the scale length (measured on each string's path from nut to bridge). If different strings have different scale lengths, calculate each one separately using its actual scale length. This is common on extended-range instruments.
The calculator provides fret center positioning only. When installing frets, the slot position accounts for the fret crown radius—typically position the slot so the fret crown center lands at the calculated distance. Consult your fret crown specifications (often 9.5-16 inches) to determine exact slot positioning relative to your calculated centers.
