Decimal to Fraction Converter

Fraction Converter

Enter any decimal in inches or millimeters. Returns the nearest imperial fraction in both directions — floor and ceiling — to any denominator you set. Exact matches are detected and highlighted automatically.

Direction
Display Mode

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Enter a dimension to convert

How It Works

Given input value v and denominator N, the converter finds the two fractions with denominator N that bracket v — one rounding down (floor), one rounding up (ceiling).

  1. Unit conversion (mm only): v_in = v_mm / 25.4. All fraction math is in inches; mm equivalents are derived.
  2. Scale to denominator: raw = v_in × N — expresses the input as a numerator over N.
  3. Floor: n_floor = floor(raw) → value = n_floor / N
  4. Ceiling: n_ceil = ceil(raw) → value = n_ceil / N
  5. Reduction: Each fraction divided by GCD(numerator, denominator). 4/16 displays as 1/4.
  6. Exact match: If |raw − round(raw)| < 1×10⁻⁹, the input is exactly representable at this denominator. The epsilon is necessary — IEEE 754 floating-point drift means 0.5 × 32 can compute as 16.000000000000004, not 16.
  7. Error: |fraction_value − v_in|, reported in the active display unit.
  8. Closest: Whichever of floor/ceiling has smaller error. Ties go to floor.

Example — exact match: 12.7 mm, 32nds. v_in = 12.7/25.4 = 0.5". raw = 0.5×32 = 16. Integer → exact match: 16/32 = 1/2". Error = 0.

Example — no match: 0.356", 16ths. raw = 0.356×16 = 5.696. Floor = 5/16 = 0.3125" (Δ 0.0435"). Ceiling = 6/16 = 3/8 = 0.375" (Δ 0.019"). Closest = 3/8".

Non-binary denominators (thirds, fifths, tenths, hundredths, thousandths) are not standard imperial callouts but are useful for decimal-inch and metric-approximation workflows.