How to calculate fret positions
Enter the open-string scale length, select millimetres, centimetres or inches, and enter 1–36 frets. Scale length is the nominal vibrating distance from nut to bridge, not the overall neck length. The initial example uses 648 mm and 24 frets.
Read From nut for each cumulative position. From previous fret is the difference between adjacent positions; for fret 1, it is the gap from the nut. To bridge is the remaining ideal vibrating length. The headline is the nut-to-fret distance for your last requested fret. The 12th-fret reference is always half the full scale, even when you request fewer than twelve frets.
The form starts with a valid example. Press Calculate immediately to run it. Focusing or first editing a numeric field clears all example numbers and any confirmed result once, while preserving new typing and unit selections. Later focus changes keep your own entries. The diagram updates with valid draft values; empty or invalid drafts retain a frame marked —. Calculate confirms the separate result and enables Copy result. Clear leaves inputs empty and never restores the example.
Formula and proportional diagram
For scale length L and fret number n, distance from the nut is dₙ = L × (1 − 2^(−n/12)). Remaining length is L × 2^(−n/12), and adjacent spacing is dₙ − dₙ₋₁, with d₀ = 0. Each fret raises the ideal frequency by a ratio of 2^(1/12). Twelve steps double the frequency and halve the vibrating length. This is the geometric basis of 12-tone equal temperament.
The diagram draws the complete scale from nut to bridge. Frets become closer together toward the bridge, rather than being placed in equally spaced cells. Only selected fret numbers are labelled to keep the diagram readable; the table contains every requested fret. On a narrow screen, scroll the diagram or table horizontally within its own area. Screen dimensions do not represent physical cutting dimensions.
Two examples
With 648 mm and 24 frets, fret 1 is 36.37 mm from the nut. Fret 12 is 324 mm from the nut, leaving 324 mm to the bridge. Fret 24 is 486 mm from the nut and leaves 162 mm. These half and quarter lengths provide simple independent checks. The 12th-fret adjacent gap is about 19.27 mm.
With 25.5 in and 12 frets, fret 1 is approximately 1.43 in from the nut and fret 12 is exactly 12.75 in. Entering the equivalent 647.7 mm gives 323.85 mm at fret 12. A unit change does not convert the typed number: it changes how that number is interpreted. Enter the converted scale length yourself, then calculate again.
Precision, editing and practical limits
Results normally show at most two decimal places, without unnecessary trailing zeroes. Very small nonzero values use scientific notation so they do not appear as zero. Calculations retain full numeric precision before display; subtracting two rounded displayed positions may differ slightly from the displayed adjacent gap. Values accept a decimal point or a decimal comma, without thousands separators.
Supported lengths are greater than zero and at most 10,000 in the chosen unit; fret counts are integers from 1 to 36. Clear empties numeric fields and results while preserving the unit. Copy result exports the same rounded table with units as plain text.
Use these ideal positions to understand spacing or compare a design. Real instruments may need compensation for string stiffness, action, tension and construction details. This page does not calculate bridge compensation, fan frets, alternative temperaments, slot width or manufacturing tolerances. It does not guarantee a cutting plan; a screen diagram is not a dimensionally calibrated template.
Frequently asked questions
Why is the 12th fret halfway along the scale?
An octave doubles frequency. For the same ideal string and tension, that requires half the vibrating length.
Why are adjacent gaps getting smaller?
Each new fret multiplies the remaining length by 2^(−1/12). The absolute reduction becomes smaller as the remaining length shrinks.
Can I enter a decimal fret count?
No. A fret count selects numbered frets, so use an integer from 1 to 36.
Does changing units convert my input?
No. The selected unit labels the entered scale length. Convert the number yourself and recalculate; old results disappear on the change.