Bike Gear Inch & Ratio Calculator - Online Cycling Tool
Calculate gear inches, meters of development, and speed ratio for any chainring/cog combination. For cyclists.
UD5 Toolkit
Calculate precise fret positions for any scale length. Essential tool for luthiers, guitar builders & repair technicians.
| Fret # | Distance from Nut | Fret Spacing | Distance from Bridge |
|---|
A fret position calculator determines the exact location of each fret on a stringed instrument's fingerboard based on the scale length (the vibrating length of the string from nut to bridge). It uses the 12-tone equal temperament formula to compute precise distances from the nut for each fret, ensuring accurate intonation across all notes.
The formula is: Distance from nut = Scale Length × (1 − 1 / 2n/12), where n is the fret number. This is derived from the 12th root of 2 (≈1.059463), the fundamental ratio of equal temperament. Each fret shortens the vibrating string by this factor, raising the pitch by one semitone. The 12th fret always falls exactly at 50% of the scale length.
Scale length is the distance from the nut to the bridge saddle — the full vibrating length of an open string. It fundamentally affects string tension, tone, and playability. Longer scale lengths (e.g., 25.5" Fender) produce brighter, snappier tones with higher tension; shorter scales (e.g., 24.75" Gibson) feel slinkier and produce warmer tones. Scale length also determines fret spacing — longer scales have wider fret spacing.
This is a direct consequence of equal temperament. Each semitone requires the string length to be multiplied by 1 / 21/12 ≈ 0.9439. Since each successive fret operates on an already-shortened length, the absolute distance between frets shrinks exponentially. The spacing at the 24th fret is only about 25% of the spacing at the 1st fret. This geometric progression ensures every semitone is perfectly in tune.
The 25.5" scale (Fender Stratocaster, Telecaster) has wider fret spacing, providing more room for complex chord fingerings in higher positions and a brighter, more articulate tone with stronger harmonics. The 24.75" scale (Gibson Les Paul, SG) offers closer fret spacing for easier stretches, a warmer midrange emphasis, and slightly less string tension — making bends easier. Many players find the shorter scale more comfortable, while others prefer the clarity of the longer scale.
Absolutely. Bass guitars use the same equal temperament system. Common bass scale lengths are 34" (standard long scale, e.g., Fender Precision/Jazz Bass), 30" (short scale), and 35" (extra-long scale for 5-string basses). Simply enter the appropriate scale length. The fret positions follow the exact same mathematical formula, just scaled to the longer string length.
The calculator provides theoretical fret positions based on ideal string behavior. In practice, strings stretch slightly when pressed to the fret, causing notes to play sharp. This is corrected by saddle compensation at the bridge — moving the saddle slightly away from the nut. The "Distance from Bridge" column in our results helps luthiers understand the vibrating length for each fretted note, which is useful when setting up intonation.
Precision is critical. An error of just 0.5mm (0.02") in fret placement can cause noticeable intonation issues, especially in higher frets where spacings are already very tight. Professional luthiers typically work to tolerances of ±0.2mm (±0.008") or better. Using a precision ruler, feeler gauges, and good lighting is essential. Many modern luthiers use CNC machines for extreme accuracy. Always double-check your measurements.
The 12th root of 2 (≈1.059463) is the mathematical constant that defines equal temperament. Multiplying any frequency by this number raises it by exactly one semitone. Multiplying 12 times yields a full octave (frequency doubles). In fret calculations, this constant determines the ratio between adjacent fret positions: each fret is placed so the remaining string length is 1/1.059463 ≈ 94.39% of the previous length. This elegant mathematical relationship ensures every key sounds equally in tune.
Start by marking the nut position on your fingerboard blank. Using a precision ruler aligned with the nut, mark each fret position using the "Distance from Nut" column. Always measure from the nut — never stack measurements (measuring each fret from the previous one) as errors will accumulate. Use a sharp marking knife for accuracy. Cut fret slots with a proper fret saw. The "Fret Spacing" column is useful for visual verification that spacing decreases smoothly. For best results, work in millimeters even for inch-based scale lengths — the finer graduations reduce rounding errors.
Electric Guitars: Fender 25.5", Gibson 24.75", PRS 25", Gretsch 24.6"
Acoustic Guitars: Martin 25.4", Gibson 24.75", Taylor 25.5"
Baritone Guitars: 27"–30"
Bass Guitars: Standard 34", Short 30", Extra-long 35"–37"
Mandolin: 13.875"–14"
Ukulele: Soprano 13.5", Concert 15", Tenor 17", Baritone 19"
Classical Guitar: Typically 650mm (25.6")
The equal temperament fret system was first mathematically described by Vincenzo Galilei (father of Galileo) in the late 16th century, though the 12th-root-of-2 rule was refined later. Before equal temperament, luthiers used various meantone and just intonation systems with irregular fret spacing. The modern system became standard in the 19th century and is now universal for fretted instruments. Interestingly, the rule of 18 (placing each fret at 1/18th of the remaining string length) was used as a practical approximation before precise calculation methods became available.
Calculate gear inches, meters of development, and speed ratio for any chainring/cog combination. For cyclists.
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