Fret Position Calculator: Distance from the Nut to Every Fret
Find the exact distance from the nut to any fret, the spacing from the previous fret and the length left to the bridge for any scale length, in mm and inches, with presets for guitar, bass, ukulele, mandolin and banjo and a full fret-slot table for building or refretting a fingerboard.
How it works
Distance from nut to fret n = L × (1 − 1 ÷ 2^(n ÷ 12)) · Gap from fret n − 1 = position(n) − position(n − 1) · To bridge = L ÷ 2^(n ÷ 12) · The 12th fret is always at L ÷ 2
Frets are placed for 12-tone equal temperament: each fret shortens the vibrating length of the string so the pitch rises one semitone, which means the length left to the bridge is divided by the twelfth root of 2 (about 1.059463) at every fret. Measured from the nut, fret n therefore sits at L × (1 − 1/2^(n/12)), where L is the scale length. The 12th fret, the octave, is always at exactly half the scale length, and the 24th fret at three quarters of it. The gaps shrink by the same factor each step, which is why high frets are packed so close together. The luthier's "rule of 17.817" is the same calculation done one fret at a time: divide the remaining length by 17.817 to get the next gap. The older rule of 18 places frets slightly too close to the nut and plays progressively flat, so it is no longer used. Choose a preset or enter your own scale length in millimetres, centimetres or inches; the table lists every slot from the nut so you can mark a fingerboard, place fretless lines or check an existing neck.
Worked example
With the default 648 mm scale (about 25.5 in), fret 12 sits at 648 × (1 − 1/2) = 324.00 mm (12.756 in) from the nut. Fret 11 is at 648 × (1 − 1/2^(11/12)) = 304.73 mm, so the 12th fret is 19.27 mm past it, and 324.00 mm of string remains to the bridge. Fret 1 is 36.37 mm from the nut, and each later gap is about 5.6% shorter than the one before.
Sources: Fret: equal temperament and the twelfth root of two (Wikipedia) · Fret placement formula, the 17.817 constant and a 25.5 in fret table (R.M. Mottola, Liutaio Mottola) · Scale length of string instruments: common guitar, bass, mandolin and banjo scales (Wikipedia)
Frequently asked questions
How do you calculate fret positions?
Use distance = scale length × (1 − 1 ÷ 2^(n ÷ 12)) for fret n. For a 25.5 in scale, fret 1 is 25.5 × (1 − 0.94387) = 1.431 in from the nut and fret 12 is 12.75 in. Measure every fret from the nut to avoid adding up errors.
Why is the 12th fret always at the halfway point?
The 12th fret produces the octave, which doubles the frequency. Doubling pitch means halving the vibrating length, so the 12th fret sits at exactly half the scale length on any fretted instrument.
What is the rule of 17.817?
It is the fret-by-fret version of the formula: divide the scale length by 17.817 to get the distance from the nut to fret 1, then divide the remaining length by 17.817 again for the next gap, and so on. 17.817 comes from 1 ÷ (1 − 2^(−1/12)). The older rule of 18 is slightly off and makes the upper frets flat.
What scale length is my guitar?
Fender Stratocasters and Telecasters use 25.5 in (647.7 mm), most Gibsons 24.75 in (628.65 mm, often measured as 24 5/8 in), PRS 25 in, classical guitars 650 mm, and long-scale basses 34 in. To measure, double the distance from the nut to the centre of the 12th fret.
Does this work for a fretless fingerboard or a ukulele?
Yes. The formula is the same for any equal-tempered fretted or lined instrument. Use the ukulele, mandolin or banjo preset, or enter the scale length, and use the table to mark the lines.
Does the bridge position change the fret positions?
No. Frets are laid out from the nominal scale length. The saddle is then set a little behind that length (compensation) so fretted notes play in tune despite the string stretching when pressed.
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This calculator is for educational purposes. Double-check important results before acting on them.