Free Fret Calculator

Overview

This fret position calculator is a free online tool built for DIY luthiers who need accurate guitar fret spacing, ukulele fret positions, or any fretted‑instrument layout based on the Western chromatic scale. Whether you are constructing a solid‑body electric guitar, a classical acoustic, a banjo, or a custom bass, simply enter your desired scale length and the calculator instantly returns the exact distance from the nut to each fret — up to the 24th fret or more. No manual algebra or reference tables required.

Understanding Frets and Their Spacing

Frets are thin metal bars inserted into the fingerboard. When a string is pressed behind a fret, its effective vibrating length is shortened, raising the pitch. For an instrument to play in tune at every position, the frets must be spaced according to a precise mathematical pattern. This pattern has its roots in the work of Pythagoras and was later standardized through the adoption of twelve‑tone equal temperament (12‑TET), which is now the universal tuning system for most Western music.

Mathematics Behind Fret Placement

The fret spacing formula combines three fundamental relationships: the Pythagorean frequency ratio, the octave‑doubling property of the chromatic scale, and the inverse law connecting string length to frequency.

1. The Constant Frequency Ratio

Pythagoras postulated that the frequencies of two adjacent notes should share a constant ratio, denoted here as $c$. If $f_0$ is the open‑string frequency and $f_n$ is the frequency when the string is pressed at the $n$-th fret, then:

$$f_n = c^n \cdot f_0 \tag{1}$$

2. Determining $c$ from the Octave

In the 12‑TET system, an octave consists of 12 equally spaced semitones, and the frequency exactly doubles after 12 steps: $f_{12} = 2 f_0$. Substituting into equation (1):

$$2 f_0 = c^{12} \cdot f_0 \;\Longrightarrow\; c = 2^{1/12}$$

Evaluating the root gives $c \approx 1.0594630943593$, commonly rounded to $1.059463$. This constant is the foundation of any fret placement calculator.

3. Physics of a Vibrating String

For an ideal string fixed at both ends, the fundamental frequency relates to its length by:

$$f = \frac{v}{2L}$$

where $v$ is the wave speed (dependent on tension and linear density). Applying this to the open string (length $L_0$) and to the $n$-th fret (length $L_n$ from fret to bridge):

$$f_0 = \frac{v}{2L_0}, \quad f_n = \frac{v}{2L_n} \tag{2}$$

4. Fret Position Formula

Combine (1) and (2). Substitute $f_n$ from (1) into the second expression of (2):

$$c^n \cdot \frac{v}{2L_0} = \frac{v}{2L_n}$$

Cancel $\frac{v}{2}$ from both sides:

$$\frac{c^n}{L_0} = \frac{1}{L_n} \;\Longrightarrow\; L_n = \frac{L_0}{c^n}$$

$L_n$ is the distance from the $n$-th fret to the bridge. For practical lutherie, measurements are usually taken from the nut. The nut‑to‑fret distance is:

$$d_n = L_0 - L_n = L_0 - \frac{L_0}{c^n} = L_0 \left(1 - \frac{1}{c^n}\right) = L_0 \left(1 - (0.9438743)^n\right)$$

The constant $0.9438743$ equals $1/c$. This single formula works for any fretted instrument that follows 12‑TET: guitars, ukuleles, mandolins, bouzoukis, or bass guitars.

Using the Fret Calculator

The tool is designed for simplicity and accuracy. Follow these steps:

1. Measure or choose your scale length. The scale length is the distance from the nut to the bridge (or the saddle). Typical values:
   • Electric guitar: 25.5 in (648 mm) or 24.75 in (628 mm)
   • Acoustic guitar: 25.4 – 25.6 in (645 – 650 mm)
   • Ukulele soprano: ~13 in (330 mm); concert: ~15 in (380 mm); tenor: ~17 in (430 mm); baritone: ~19 in (480 mm)
   • Bass guitar: 34 in (864 mm) or 35 in (889 mm) You may also enter a custom value.
2. Select the desired number of frets (typically 12, 22, or 24). The calculator will compute positions for each.
3. Get instant results. Below is an example output for a 25.5 in guitar scale (frets 1–10):

Fret	Distance from Nut (in)
1	1.43
2	2.78
3	4.06
4	5.26
5	6.40
6	7.47
7	8.49
8	9.46
9	10.38
10	11.26

For a 17 in tenor ukulele, the first ten fret positions are:

Fret	Distance from Nut (in)
1	0.95
2	1.85
3	2.71
4	3.51
5	4.27
6	4.98
7	5.66
8	6.31
9	6.92
10	7.50

All values are calculated using the exact formula $d_n = L_0 (1 - 2^{-n/12})$. You can switch between inches and centimeters in the calculator interface.

4. Transfer the measurements. Mark each distance on your fretboard with a sharp pencil or knife, using a precision ruler or digital caliper. Double‑check the 12th‑fret position (which should be exactly half the scale length) as a sanity check.
5. Install the frets. Cut slots at the marked positions, insert the fret wire, and trim.

Whether you need a quick ukulele fret calculator or a full guitar fret spacing guide for a multi‑scale instrument, this free online tool delivers reliable data in seconds. It gives DIY guitar fret positions with the same accuracy used by professional luthiers.

Additional Tips

• Always measure from the nut toward the bridge; the distances are cumulative but the formula directly gives the nut‑to‑fret value.
• For instruments with a compensated saddle, the scale length used in the calculator should be the nominal uncompensated length (usually the string length from the nut to the 12th fret times 2).
• The calculator follows equal temperament; if you intend to use a different temperament (e.g., just intonation), the positions will differ.