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
How we build and check this calculator
This calculator runs entirely in your browser, so the numbers you enter stay on your device. The math behind it is written by hand and tested against worked examples and standard references before the page goes live.
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