Fret Calculator - Equal-temperament distance from nut

A fret calculator is a luthier layout tool that returns the distance from the nut to any fret on a guitar, bass, or ukulele from a single scale-length input, using the equal-temperament constant 2^(1/12). A fret calculator turns one scale-length number into a complete fret map without a paper table.

• • Setting a guitar neck: Lay out fret slots on a new neck for a Stratocaster, Les Paul, or extended-range build before you cut.
• • Refretting an existing instrument: Recreate original spacing on a vintage guitar or convert a 21-fret neck to 22 frets without changing the scale length.
• • Comparing scale lengths: See how the same fret number moves when you switch from a 25.5 in Fender scale to a 24.75 in Gibson scale or a 34 in bass scale.
• • Planning ukulele or bass builds: Run short-scale (13 to 17 in) or long-scale (30 to 36 in) layouts through the same equal-temperament math as a six-string.

The distance from the nut to the 12th fret is always exactly half the scale length under equal temperament, which is why the same calculator covers 13.5 in ukuleles, 25.5 in electric guitars, and 34 in bass guitars with no special cases.

When you switch between inches and centimeters the result panel keeps the underlying scale length unchanged, the same way the Data Storage Converter keeps byte counts unchanged while changing the unit label.

The calculator applies one geometric series to the scale length: each fret cuts the remaining vibrating string by a factor of the 12th root of 2 (~1.059463), so the distance from the nut grows by a smaller and smaller amount as fret numbers rise.

• scaleLength: Vibrating string length from the nut to the bridge, in the chosen unit.
• n (fretNumber): Integer fret number, 1 through 27.
• 2^(1/12): Equal-temperament semitone ratio, ≈ 1.059463.

The spacing to the previous fret is the difference between two consecutive distanceFromNut values, so a Stratocaster jumps 1.431 in to fret 1 but only 0.758 in to fret 12 and 0.368 in to fret 24.

According to Liutaio Mottola Lutherie (Calculating Fret Positions), the equal-temperament distance from the nut for fret n is scaleLength × (1 - 2^(-n/12)), which puts the 12th fret of a 25.5 in scale at exactly 12.75 in (half the scale length)

Because the equal-temperament ratio is geometric along the string, the same logarithm that powers a Log 2 Calculator also powers the distance-to-fret formula here.

Four building blocks drive the math behind every fret position on a modern fretted instrument.

These four ideas combine into one geometric series; you do not need to remember any number beyond the scale length once you have chosen the formula.

If you want to see how shorter vibrating string length at each fret translates to a higher pitch, pair the fret distance with a Frequency Calculator.

Enter your instrument's scale length, switch to the unit you build with, pick a target fret, and read the layout straight off the result panel and reference table.

1. 1 Measure or look up the scale length: Use the manufacturer's spec (25.5 in for a Strat, 24.75 in for a Les Paul, 34 in for a standard bass) or measure from the nut to the centerline of the 12th fret and double the result.
2. 2 Pick inches or centimeters: Use the dropdown to match the ruler or CNC template you work with. The internal math is unit-independent because the 12th root of 2 is dimensionless.
3. 3 Choose a target fret: Pick the fret you are laying out right now (1 to 27). The reference table fills every fret below it so you can mark slots in order without re-entering numbers.
4. 4 Mark and cut: Mark the distance-from-nut result on your fretboard, scribe the slot, then move to the next fret using the spacing column instead of re-measuring from the nut.
5. 5 Watch the octave marker: When the target fret is 12, 24, or 36, the octave marker flips to 1 and the spacing from the previous fret halves, which is a quick sanity check on a long layout.
6. 6 Verify with a different scale length: Switch the scale length to compare how a 25.5 in scale differs from a 25 in scale at the same fret number before committing to a final neck design.

To lay out a 22-fret Stratocaster neck at 25.5 in: leave the unit on inches, set the scale length to 25.5, choose target fret 1 to mark the first slot at 1.431 in from the nut, then increment the target fret to read each subsequent distance off the result panel (3.748 in at fret 3, 5.487 in at fret 5, 7.073 in at fret 7).

Use the live update on every input the same way you would scan pages per minute in a Book Reading Calculator, so the per-fret table redraws as soon as you change the scale length.

Five practical gains when you move fret placement from a paper table to this live calculator.

• • Cut straight to the right number: Skip the per-fret constant table and get a 3-decimal-place distance from the nut the moment you enter the scale length and fret number.
• • See the octave boundary at a glance: The octave marker (1 at frets 12, 24, and 36) tells you when the geometry repeats, so you can double-check a layout in seconds instead of measuring twice.
• • Switch units without re-entering: Change the unit dropdown from inches to centimeters and the result panel and reference table re-render in the new unit without losing the underlying scale length.
• • Plan with a full reference table: The reference table lists every fret distance up to 12, 20, 22, 24, or 27 frets so you can mark a whole neck in one pass instead of one fret at a time.
• • Compare instruments on the same scale: Toggle the scale length between 24.75 in (Les Paul), 25.5 in (Stratocaster), and 30 in (baritone) to see how the same fret number moves before you commit to a build.

These benefits compound when you are doing more than one layout in a session: the calculator keeps the equal-temperament constant hidden and lets you focus on the build itself.

For determining whether a fret is on a 12-fret octave boundary without leaving the page, a Modulo Calculator on fretNumber mod 12 reproduces the octave flag in the result panel.

Three inputs shape the output and three approximations bound how far you can push the formula before a real neck needs compensation.

• • The calculator models ideal geometry, not real-world fret compensation; under saddle and bridge saddle compensation (typically 1 to 3 mm per string) is applied at the bridge, not the nut, and is outside the equal-temperament formula.
• • For non-equal-temperament tunings (just intonation, historical temperaments) the per-fret ratio is not constant, so this calculator is not the right tool for those layouts.

Treat the result as the nominal fret position and adjust for compensation at the bridge.

According to Wikipedia (Fret article), equal temperament assigns every adjacent pair of frets a frequency ratio of the twelfth root of two (~1.059463), so the 12th fret divides the open-string length into two exact halves

When you want to see why every fret is a constant 2^(-1/12) step along the vibrating string, the Geometric Sequence Calculator plots the same geometric series for any first term and common ratio, so the equal-temperament factor card stays consistent with the math.