Fret Spacing Calculator: Formula & How to Use

A fret spacing calculator works out the distance from the nut to each fret (or between frets) on a guitar or other fretted instrument. You enter the scale length and the number of frets, and it returns the position of every fret along the fingerboard, usually in inches or millimetres.

Formula

The standard formula for fret placement is based on the equal-tempered scale, where each semitone has a frequency ratio of the 12th root of 2 (about 1.059463). The distance from the nut to the n-th fret is:

D_n = L × (1 − 2^−n/12)

• D_n – distance from the nut to fret n (mm or inches)
• L – scale length, the distance from nut to bridge (same unit as D)
• n – fret number (1, 2, 3, …)

The distance between two consecutive frets is simply D_n − D_n−1. This formula assumes a perfectly straight string and no compensation at the bridge – real instruments need slight adjustments, but the formula gives the theoretical positions used as a starting point.

Worked Example

Using the calculator defaults: scale length = 650 mm, number of frets = 24.

For fret 1: D₁ = 650 × (1 − 2^−1/12) = 650 × (1 − 0.943874) = 650 × 0.056126 = 36.48 mm.

For fret 12: D₁₂ = 650 × (1 − 2^−12/12) = 650 × (1 − 0.5) = 325.0 mm – exactly half the scale length.

For fret 24: D₂₄ = 650 × (1 − 2^−24/12) = 650 × (1 − 0.25) = 487.5 mm.

The calculator outputs the positions for all 24 frets, each rounded to 2 decimal places. The 12th fret at 325.00 mm matches the expected midpoint.

Why Fret Spacing Matters

Fret positions determine whether each note plays in tune. If the frets are even slightly off – a fraction of a millimetre – the pitch error becomes audible, especially on higher frets. Luthiers and hobbyists use fret spacing calculators to lay out fingerboards before cutting slots. The equal-tempered system is universal on modern instruments, so the same formula applies to guitars, basses, mandolins, ukuleles, and even some historical fretted instruments that use equal temperament.

How to Choose Your Scale Length

The scale length is the most important input. It is the distance from the nut to the bridge, measured along the string path. Common values:

• Electric guitar: 25.5 inches (648 mm) or 24.75 inches (629 mm)
• Acoustic guitar: 25.4 inches (645 mm) typical
• Bass guitar: 34 inches (864 mm) common
• Ukulele: 17 inches (432 mm) or 15 inches (381 mm)

If you are building a custom instrument, decide the scale length first based on string tension and playability. The fret positions scale linearly with scale length – double the scale length and all fret distances double.

Common Mistakes and Misconceptions

One common mistake is measuring the scale length from the nut to the 12th fret and doubling it – that gives the theoretical scale length, but actual instruments often have compensation at the bridge, so the real scale length may be a few millimetres longer. Another mistake is using the 18.0 rule (dividing by 18) instead of the exact 17.817 factor. The old rule gives slightly different positions, which can cause intonation errors on the upper frets.

Also, many people forget that the formula gives positions from the nut, not from the previous fret. If you are cutting slots, you need the cumulative distances, not the individual gaps.

Limits of the Formula

The formula assumes a perfectly flexible string and no string height. In reality, pressing a string down stretches it slightly, so the actual speaking length is a bit longer. Luthiers compensate by moving the bridge or adding a slight offset to the nut. The formula also ignores the thickness of the fret wire – the actual point where the string touches the fret is the centre of the fret crown, so you must subtract half the fret width when cutting slots.

For most DIY projects, the theoretical positions are accurate enough. For professional concert instruments, builders often use a strobe tuner to fine-tune the intonation after assembly.

Alternatives to a Fret Calculator

If you don’t have a calculator, you can use a pre-printed fret template or a commercial fret slotting jig. These are physical guides that you place on the fingerboard and use to saw the slots. They are convenient but limited to specific scale lengths. Some people use a spreadsheet with the formula, which gives the same results as this calculator. The advantage of an online calculator is that it works for any scale length and any number of frets, and it shows the formula so you can verify the numbers.

Frequently Asked Questions

What is the rule of 18? The rule of 18 is a historical approximation where the scale length is divided by 18 to get the first fret distance, then the remaining length is divided by 18 again, and so on. The exact divisor is 17.817 (1 / (2^(1/12) − 1)). The rule of 18 gives slightly wider fret spacing, which was used before precise equal temperament became standard.

Do I need to compensate for the nut? Yes, in practice. The formula assumes the string vibrates from the nut to the bridge, but when you press a string, it stretches and the pitch goes sharp. Adding a small amount of compensation (usually 1–2 mm at the bridge, and sometimes a compensated nut) helps correct this. The calculator gives the theoretical positions, not the final intonation settings.

Can I use the same formula for a bass guitar? Yes, the formula is identical. Just enter the bass scale length (e.g., 864 mm) and the number of frets. The physics of vibrating strings is the same regardless of instrument type.

What if my scale length is in inches? You can enter inches directly, but the calculator expects a number. If you enter 25.5, the output will be in inches. Just be consistent – don’t mix units.

Why is the 12th fret exactly half the scale length? Because a note one octave higher has exactly double the frequency. The string length must be halved to double the frequency, so the 12th fret sits at the midpoint of the scale length. This is a good check for your calculations.

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in sl | Scale length | mm | 650 | 0
in nf | Number of frets | - | 24 | 0
out pos | Fret positions from nut | mm | sl * (1 - pow(2, -seq / 12)) | 2