Guitar Fret Spacing Calculator (12th Root of 2)
Calculate fret positions on a guitar or bass by scale length.
Get exact distances from nut for all 24 frets using the 12th root of 2 equal-temperament formula.
Guitar Fret Spacing
Fret positions on any string instrument follow the 12th root of 2 rule. Each fret raises the pitch by one semitone — exactly the 2^(1/12) frequency ratio.
The formula: Distance from nut to fret N = Scale length × (1 - 1 / 2^(N/12))
Or equivalently: Position = Scale × (1 - 0.943874^N)
Standard scale lengths:
| Instrument | Scale Length |
|---|---|
| Fender Stratocaster, Telecaster | 25.5 in (648 mm) |
| Gibson Les Paul, SG | 24.75 in (628 mm) |
| Gibson 25.5 long-scale | 25.5 in |
| PRS standard | 25 in (635 mm) |
| Fender Mustang, Jaguar | 24 in (610 mm) |
| Fender Bass (P-Bass, Jazz) | 34 in (864 mm) |
| Short-scale bass | 30 in (762 mm) |
| Classical guitar | 25.6 in (650 mm) |
| Mandolin | 13.875 in (352 mm) |
| Banjo (5-string) | 26.25 in (667 mm) |
| Ukulele (soprano) | 13.5 in (343 mm) |
| Ukulele (concert) | 14.75 in (375 mm) |
| Ukulele (tenor) | 17 in (432 mm) |
Why the 12th root of 2?
- 12 semitones per octave
- An octave = doubling of frequency
- Each semitone must equal 2^(1/12) = 1.0594631 ratio
- Fret position is “scale × (ratio - 1) / ratio” iteratively, simplified to the formula above
Position to fret 12 (the octave): Always exactly half the scale length.
For a 25.5" Strat: 12th fret is at 12.75 inches from the nut.
Compensation considerations:
- Real-world fretboards don’t use pure formula spacing — bridge compensation accounts for string stiffness
- Saddle is set 0.04-0.10 in BACK from the calculated 12th-fret-doubled position
- Each string compensates differently (heavy E more than light B)
Fanned-fret guitars: Modern multiscale guitars use different scale lengths for each string:
- Bass strings: longer scale (better low-string tone, less floppy)
- Treble strings: shorter scale (easier playing, brighter)
- Frets fan from one scale to another
Common scale length effects:
| Scale | Tone Effect |
|---|---|
| Long (25.5"+) | Tighter strings, brighter, snappier |
| Medium (25") | Balanced |
| Short (24.75" Gibson) | Warmer, looser feel, easier bending |
| Very short (24" Mustang) | Wobbly feel, very mellow |
Building your own fretboard:
- Use a digital caliper for accuracy (±0.005 in)
- Mark fret positions with a sharp scribe
- Cut slots before gluing fretboard to neck
- Pre-test with paper templates first
- Allow ±0.001 in tolerance — hand-cut frets within 0.005 in are still musically acceptable