Guitar Fret Spacing Calculator - Fret Position Formula

What is a guitar fret spacing calculator?

A guitar fret spacing calculator finds the distance from the nut to each fret on a guitar neck, based on the instrument's scale length. It uses the equal temperament formula, the mathematical rule that divides a musical octave into 12 equal steps. Luthiers, guitar builders, and hobbyists use it to mark accurate fret positions before cutting slots into a fingerboard.

How to calculate fret spacing

Each fret shortens the vibrating length of a string by a fixed ratio, not a fixed distance. The ratio between one fret and the next is the twelfth root of two:

$r = 2^{1/12} \approx 1.059463$

Twelve semitones multiplied together double the frequency, which is one octave. Using this ratio, the distance from the nut to fret number n is:

$d_n = L \times \left(1 - \frac{1}{2^{n/12}}\right)$

• $d_n$ is the distance from the nut to fret n
• $L$ is the scale length: the vibrating length of the string, measured from the nut to the point where the string meets the bridge saddle
• $n$ is the fret number, counting up from 1 at the nut end

Because the divisor grows with each fret, the physical gap between frets shrinks steadily moving toward the bridge. Fret 1 sits at about 5.6% of the scale length. Fret 12, the octave fret, sits exactly halfway between the nut and the bridge.

Worked example: 25.5-inch scale length

A 25.5-inch (64.77 cm) scale length is the standard used on Fender Stratocasters and Telecasters. The table below shows the distance from the nut to each of the first six frets, and the gap between each fret and the one before it.

Fret 5, worked in full:

$d_5 = 25.5 \times \left(1 - \frac{1}{2^{5/12}}\right) = 25.5 \times 0.25085 = 6.397"$

At fret 12 the distance from the nut works out to 12.750 inches, exactly half of the 25.5-inch scale length. That matches fret 12 marking the octave, one full doubling of frequency above the open string.

How to use this calculator

1. Enter the scale length of the instrument.
2. Choose inches or centimeters as the unit.
3. Enter the number of frets to calculate, from 1 to 24. A larger number is reduced to 24.
4. Read the distance from the nut and the gap from the previous fret for each row of the results table.
5. Copy the table or download it as a text file to use while marking the fingerboard.

Common scale lengths

• Fender Stratocaster and Telecaster: 25.5 in (64.77 cm)
• Gibson Les Paul and SG: 24.75 in (62.865 cm)
• PRS guitars: 25 in (63.5 cm)
• 4-string bass guitar: 34 in (86.36 cm)
• 5-string bass guitar: 35 in (88.9 cm)

A longer scale length raises string tension at a given pitch, which tends to give a brighter tone and tighter bass response. A shorter scale length lowers tension, which many players find easier to fret and bend.

The Rule of 18

Before calculators, luthiers approximated fret spacing with a shortcut called the Rule of 18: divide the remaining string length by 18 to estimate the next fret. It comes close for the first few frets but drifts further from the correct equal-tempered position on higher frets, so builders today use the exact formula instead.

Frequently asked questions

What is scale length?

Scale length is the vibrating length of a guitar string, measured from the nut to the point where the string meets the bridge saddle. It is the single measurement that every fret position is calculated from.

Why does fret spacing get smaller toward the bridge?

Each fret divides the remaining string length by the same ratio, not the same distance. Since the remaining string gets shorter after every fret, an equal ratio produces a shrinking physical gap as the frets approach the bridge.

Can this formula be used for a bass or a ukulele?

Yes. Any fretted instrument tuned in equal temperament uses the same formula. Enter the instrument's own scale length and the calculator returns its fret positions.

How accurate do fret positions need to be?

Builders aiming for correct intonation typically work to within about 0.01 inches (0.25 mm). Machine-cut fret slots can hold tolerances closer to 0.001 inches.

What is a multiscale, or fanned-fret, guitar?

A multiscale guitar uses a different scale length for each string, longer on the bass side and shorter on the treble side. The frets run at an angle across the neck because each string needs its own set of fret positions.

Does the calculator account for bridge compensation?

No. It returns the theoretical fret positions based on the nominal scale length only. In practice, luthiers shift the bridge saddle back slightly to compensate for the string stretching when it is pressed down, which this calculator does not calculate.