ClutchCalcs

Math

Fraction Calculator

Need to add 3/8" + 5/16" for a woodworking layout? Multiply 2 1/2 by 1 1/4 for a recipe? Subtract 7/16 from 1 1/8 for a measurement adjustment? Fractions are everywhere in construction, baking, sewing, and any project involving imperial measurements. This calculator handles addition, subtraction, multiplication, and division of fractions — with or without whole-number parts (mixed numbers). Always reduces results to lowest terms. Shows the decimal equivalent too. No more pencil-and-paper LCM math when you're standing at a tablesaw.

Leave the whole number blank for a pure fraction. Numerator/denominator must both be filled.

Fill in both fractions to see the result.

Real-world applications

  • Carpentry / woodworking: adding/subtracting fractional inches for layouts. Cutting a 3/4" board off a 24 1/2" piece leaves 23 3/4".
  • Sewing: combining seam allowances (5/8" + 5/8" = 1 1/4" total).
  • Cooking / baking: scaling recipes — 1/4 cup × 3 = 3/4 cup.
  • Plumbing: pipe diameter math. 1/2" ID + 1/8" wall × 2 = 3/4" OD.
  • Electrical: conduit fill math (typically decimals, but old codes used fractions).
  • Construction layout: dividing a wall into equal parts. 8 ft (96") ÷ 3 studs = 32" each.
  • Stock market math: rare now since US markets use decimals, but international markets sometimes still quote in fractions.

The math behind it

Addition / subtraction: find common denominator. 1/4 + 1/3 = 3/12 + 4/12 = 7/12. Or: (n₁ × d₂ ± n₂ × d₁) / (d₁ × d₂), then reduce.

Multiplication: multiply numerators, multiply denominators. 1/4 × 1/3 = 1/12. Or: (n₁ × n₂) / (d₁ × d₂), then reduce.

Division: multiply by the reciprocal. 1/4 ÷ 1/3 = 1/4 × 3/1 = 3/4.

Mixed numbers: convert to improper fractions first. 2 1/4 = (2 × 4 + 1) / 4 = 9/4. Calculate, then convert back.

How to use this calculator

  1. First fraction: optional whole number, then numerator and denominator.
  2. Pick operation: +, -, ×, ÷.
  3. Second fraction: same format.
  4. Output: result as fraction (mixed number when applicable) + decimal equivalent.
  5. Leave whole number blank for pure fractions. Numerator and denominator must both be filled.

Common scenarios

Cut list: 8 ft board minus 24 3/8" minus 12 5/16". 8 ft = 96". 96 - 24.375 - 12.3125 = 59.3125" = 59 5/16". Useful for utilization estimation.

Doubling a 3/8 cup recipe. 3/8 × 2 = 6/8 = 3/4 cup.

How many 11 1/4" pieces from a 96" board? 96 ÷ 11.25 = 8.53 pieces — you get 8 with significant offcut. Multiply 8 × 11 1/4 = 90", so 6" left over.

FAQ

What's a mixed number? +
A whole number combined with a fraction: 2 1/2, 5 3/4, 1 1/8. Standard for carpentry measurements ("give me 3 5/8 inches"). Type the whole number in the whole-number slot, fraction parts in numerator/denominator.
Why does the result show as a fraction AND a decimal? +
Fractions are exact (especially for repeating decimals like 1/3 = 0.333...). Decimals are easier to read at a glance. Some calculators round to 6 places; results within tolerance are exact, others approximate.
Can I get a negative result? +
Yes — negative fractions are supported. Type the minus on the whole number or numerator. 3/4 - 1 = -1/4.
What's the lowest common denominator? +
The smallest number both denominators divide evenly into. For 1/4 + 1/6: LCD is 12 (smallest multiple of both 4 and 6). 1/4 = 3/12; 1/6 = 2/12; sum = 5/12. The calculator handles this automatically.
What's an improper fraction? +
A fraction where numerator ≥ denominator. 9/4, 13/8, 7/3 are improper. Improper fractions are easier for calculation (no separate whole-number handling); mixed numbers are easier to read. 9/4 = 2 1/4.
How do I add fractions with different denominators? +
Find a common denominator. For 1/3 + 1/4: common = 12. 1/3 = 4/12, 1/4 = 3/12, sum = 7/12. The calculator does the LCD math automatically; humans usually use the cross-multiplication shortcut (a/b + c/d = (ad+bc)/bd).
Why is fraction math harder than decimal math? +
Decimals can be entered into any pocket calculator. Fractions require common-denominator arithmetic, which is mental-load-heavy. In imperial-units work (US construction), fractions are the native format, so the math is unavoidable. Decimal calculators don't show 3/4 if you'd want to read it that way at the saw.
Can I use this for fractions involving units? +
Yes — the math works regardless of whether the fractions represent inches, cups, pounds, or any other unit. Just keep the same unit throughout. The calculator gives you a fraction; you interpret the units.