Music Performance
Calculate fret spacing using the 17.817 constant method.
Commonly used by luthiers for manual layouts.
The fret distance 17.817 calculator determines the physical distance from the guitar's nut to any specific fret using the geometric series formula derived from equal temperament tuning. The 17.817 constant represents the ratio used in luthier calculations to position frets accurately on a fretboard. This calculator is essential for guitar builders, repair technicians, and musicians who want to understand the mathematical foundation of fret placement. Rather than measuring by ear, luthiers rely on this precise formula to ensure each fret produces the correct pitch when played. The constant comes from the 12th root of 2 (approximately 1.0594630943592953), which defines the semitone ratio in Western music. Understanding this relationship helps builders create instruments with perfect intonation and guides repairs or custom builds.
The calculator uses an iterative algorithm that divides the remaining string length by 17.817 for each successive fret. Starting from the nut, it calculates the distance needed for the first fret, then subtracts that from the remaining length and repeats for subsequent frets. Each iteration produces a smaller fret spacing as you move up the neck, following the exponential nature of the musical scale. The algorithm outputs three values: distance from the nut (cumulative), distance from the previous fret (incremental), and remaining length toward the bridge. This method ensures that each fret position maintains the correct frequency relationship with others.
For each fret n: Distance = (Remaining Length) / 17.817. The cumulative distance from nut = sum of all previous distances. The algorithm iterates from fret 1 to the target fret number. The constant 17.817 derives from the 12th root of 2, representing the frequency ratio between semitones in equal temperament tuning.
The 17.817 constant is derived from the 12th root of 2 (≈1.05946), which defines the frequency ratio between semitones in equal temperament tuning. Inverting this ratio (1/1.05946 ≈ 0.94387) and using it in the geometric series calculation for fretboard layout gives us approximately 17.817 as a practical divisor for calculating fret positions.
Fret spacing decreases exponentially because the frequency intervals between notes are exponential, not linear. Each fret represents one semitone, and a semitone always corresponds to the same frequency ratio regardless of which octave you're in. This exponential relationship means the physical distance must also decrease proportionally—the 12th fret (one octave) sits at exactly half the scale length.
Yes, this calculator works for any fretted instrument with a straight fretboard and equal temperament tuning, including guitars, basses, mandolins, and banjos. You only need to input the correct scale length for your instrument. However, it does not account for compound fretboard radius or custom temperaments like just intonation.
Fret placement typically requires accuracy to within 0.5mm (0.02 inches) to maintain playability and intonation. Always convert calculator results carefully between measurement systems (inches to metric) and include tolerance for the width of the fret saw blade when cutting slots. Professional luthiers often use digital calipers and templates to verify results.
