Guitar Fret Spacing Calculator (12th Root of 2)

Guitar Fret Spacing

Fret positions on any string instrument follow the 12th root of 2 rule. Each fret raises the pitch by one semitone, which is 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:

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
• So the string left ringing at fret N is 1/2^(N/12) of the full scale, and the distance from the nut is whatever is left over, which is the formula above

The rule of 17.817

Luthiers cutting slots by hand rarely reach for a logarithm. They use the running form instead: measure the remaining length from the current fret to the bridge, divide by 17.817, and that is where the next slot goes. It falls straight out of the same math, since 1 - 1/2^(1/12) = 1/17.817.
The old rule of 18 is the same trick with a rounder number, and it is why some older instruments run flat higher up the neck. Divide by 18 instead of 17.817 and the error compounds: by the 12th fret the octave sits about 12 cents flat, which is an eighth of a semitone and plainly audible against an open string.

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 fretboards do not sound in tune at pure formula spacing, because pressing a string down stretches it slightly sharp. Bridge compensation is the correction
• The saddle sits 0.04 to 0.10 in BACK from the doubled 12th-fret distance
• Each string compensates differently. The wound low E needs the most, the plain B usually the least

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:

Building your own fretboard:

• Measure with a digital caliper, not a ruler
• Mark fret positions with a sharp scribe, and always measure from the nut rather than from the last fret. Fret-to-fret measuring stacks every small error into the top of the neck
• Cut slots before gluing the fretboard to the neck
• Pre-test with paper templates first

On tolerance: aim for ±0.001 in, because that is what a caliper and a careful hand can actually hold. Anything inside ±0.005 in is still musically fine. On a 25.5 in scale that much error works out at about 0.7 cents at the 12th fret and still under 1.5 cents at the 24th, well below what anyone hears. The gap between those two numbers is your margin for the slot that wanders.