Fret positions on a guitar, bass, ukulele or mandolin follow one simple formula. Luthiers and builders use it to slot a new fretboard, and players use it to check intonation. This calculator applies it to any scale length.
The formula
In equal temperament, each fret raises the pitch by one semitone, which is a frequency ratio of 2^(1/12). The vibrating length must shorten by the same ratio, so the distance from the nut to fret n is:
distance = scale length × (1 − 2^(−n/12))
On a 25.5 in scale:
- the 1st fret sits 25.5 × (1 − 0.9439) = 1.431 in from the nut;
- the 12th fret, one octave up, sits at exactly half the scale, 12.75 in;
- the 24th fret sits at three quarters of the scale.
The gap between frets shrinks as you go up the neck: about 1.43 in between the nut and the first fret, but only 0.76 in between frets 11 and 12.
The old rule of 17.817
Luthiers used to compute frets with a constant: divide the remaining length by 17.817 to find the next fret. It gives the same result, since 17.817 = 1 ÷ (1 − 2^(−1/12)). The older rule of 18 places frets slightly flat.
Common scale lengths
| Instrument | Scale length |
|---|---|
| Fender-style electric guitar | 25.5 in (648 mm) |
| Gibson-style electric guitar | 24.75 in (629 mm) |
| Classical guitar | about 25.6 in (650 mm) |
| Electric bass | 34 in (864 mm) |
| Tenor ukulele | 17 in (432 mm) |
Compensation and intonation
The formula assumes an ideal string. Real strings go sharp when pressed, because pressing stretches them. That is why bridges set the saddles slightly behind the theoretical scale length, more for the thicker strings: the compensation is often a few hundredths of an inch to about ⅛ in. Set it by tuning the open string and comparing with the 12th fret note: if the fretted note is sharp, move the saddle back.
Building tips
- Measure each fret from the nut, not from the previous fret, to avoid adding up errors.
- Slot with a fret saw that matches the tang of your fret wire.
- A fret-slotting template or a CNC-cut board guarantees accuracy for a first build.