Fret Calculator

Find the exact distance to any fret on a guitar, bass, ukulele, or other fretted instrument using the standard 12th-root-of-2 equal temperament formula.

Quick Facts

Formula
d = L − L / 2^(n/12)
L is scale length, n is the fret number, d is distance from the nut (12th-root-of-2 equal temperament).
Octave check
Fret 12 = exactly half the scale length
Because 2^(12/12) = 2, this is the standard way luthiers verify a fret layout.
Common scale lengths
Fender-style: 25.5 in (648 mm); Gibson-style: 24.75 in (629 mm)
Bass guitars commonly use 34 in (864 mm); ukuleles vary from about 13 to 21 in.

Your Results

Calculated
Distance from nut
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Nut to target fret
Distance from bridge
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Target fret to bridge/saddle
Fret width
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Spacing from the previous fret
12th fret (octave point)
-
Should equal half the scale length

Ready

Enter scale length and a target fret, then press Calculate.

About the Fret Calculator

This tool places frets on a guitar, bass, banjo, mandolin, ukulele, or any other fretted instrument using the same math that luthiers and instrument manufacturers rely on: the equal temperament (12th root of two) formula. Give it a scale length and a target fret number, and it returns the exact distance from the nut, the distance from the bridge, the width of that individual fret, and the octave check point.

The formula

For a scale length L (the vibrating string length measured from the nut to the bridge/saddle) and fret number n, the distance from the nut to that fret is:

d = L − L / 2(n/12)

Equivalently, the distance from the bridge back to fret n is simply L / 2(n/12). This formula comes from 12-tone equal temperament tuning, where each half-step (fret) raises the pitch by a constant frequency ratio of the twelfth root of two, approximately 1.059463. Because frequency is inversely proportional to vibrating string length, each fret's remaining distance to the bridge is a constant fraction, 1/2(1/12) (about 94.39%), of the previous fret's remaining distance — in other words, each fret closes roughly 5.61% of the remaining gap to the bridge.

Why the 12th fret matters

Because an octave is 12 equal half-steps, 2(12/12) = 2 exactly. That means the distance from the nut to the 12th fret is always precisely half the scale length, on any instrument, regardless of string count or tuning. Builders use this as a fast sanity check: measure nut-to-12th-fret, double it, and compare against the intended scale length. If they don't match, something in the layout is off.

Typical scale lengths

  • Fender-style electric guitar: 25.5 in (648 mm)
  • Gibson-style electric guitar: 24.75 in (629 mm)
  • Classical/nylon-string guitar: about 25.6-26 in (650-660 mm)
  • Bass guitar (long scale): 34 in (864 mm)
  • Ukulele: roughly 13 in (soprano) to 21 in (baritone)
  • Mandolin: about 13.9-14 in (350-356 mm)

How to use the result

Measure your scale length first (nut edge to the exact point where the string breaks over the bridge/saddle), enter it, then step through fret numbers one at a time if you are marking a full fretboard by hand. Many builders use a printed or CNC fret-slotting template rather than measuring each fret manually, since compounded rounding error from a ruler can throw off intonation over 20+ frets — but the underlying math is exactly this formula either way.

Frequently Asked Questions

What formula do luthiers use to place frets?
Nearly every modern fretted instrument uses the equal temperament (12th root of two) formula: d = L − L / 2^(n/12), where L is scale length, n is the fret number, and d is the distance from the nut. This spaces the 12 frets of an octave so each half-step is a constant frequency ratio apart.
Why does the 12th fret always sit at half the scale length?
An octave equals 12 equal-tempered half steps, and the formula is built so that 2^(12/12) = 2. That makes the distance to fret 12 exactly half the scale length on any instrument, which is why builders use it as a quick accuracy check when fretting a neck.
Does the formula change for bass, ukulele, or mandolin?
No. The 12th-root-of-2 formula is the same for any fretted instrument tuned to standard 12-tone equal temperament, regardless of string count or scale length. Only the scale length input changes — a ukulele might use 13 to 21 inches while a bass guitar might use 30 to 35 inches.

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