Mixed Number Calculator

A mixed number combines a whole number with a proper fraction, like 2 3/4, meaning two full units plus three-quarters of another. Tape measures, lumber tags, and recipe cards almost always show measurements this way because it is faster to read than an improper fraction: "2 3/4 inches" tells you at a glance that you are just under 3 inches, while "11/4 inches" takes an extra step to picture.

Improper fractions, where the numerator is equal to or larger than the denominator, like 11/4, represent the exact same value but are easier for arithmetic. This calculator gives you both: the mixed number for reading and the improper fraction for calculating. That distinction matters most when a plan or spec sheet mixes formats: some drawings list only improper fractions to keep the math simple for CNC software, while a field crew might want the mixed-number version to read directly off a tape measure.

Multiply the whole number by the denominator, then add the numerator, and keep the same denominator. For 2 3/4: 2 × 4 = 8, plus 3 = 11, so the improper fraction is 11/4. For 5 3/16: 5 × 16 = 80, plus 3 = 83, giving 83/16.

This works because the whole number is really just extra fractional pieces of the same size. 2 whole units, each cut into 4 quarters, hold 8 quarters total, and adding the extra 3 quarters gives 11 quarters, which is 11/4.

Divide the fraction's numerator by its denominator, then add the whole number. For 2 3/4: 3 ÷ 4 = 0.75, plus 2 = 2.75. For 5 3/16: 3 ÷ 16 = 0.1875, plus 5 = 5.1875.

To get millimeters, multiply the decimal result by 25.4. 2.75 inches × 25.4 = 69.85 mm. 5.1875 inches × 25.4 = 131.7625 mm. The calculator above shows all of these values as soon as you enter the whole number, numerator, and denominator.

Divide the numerator by the denominator and keep the remainder as the new numerator. For 17/4: 17 ÷ 4 = 4 with a remainder of 1, so the mixed number is 4 1/4. For 29/8: 29 ÷ 8 = 3 with a remainder of 5, giving 3 5/8.

The quotient becomes the whole number and the remainder sits over the original denominator, unsimplified until you check its GCD. For a deeper look at why fractions like 6/8 and 3/4 describe the same length, see the equivalent fractions calculator.

1 1/2 = 3/2 = 1.5 inches = 38.1 mm. 3 5/8 = 29/8 = 3.625 inches = 92.075 mm. 5 3/16 = 83/16 = 5.1875 inches = 131.7625 mm. 4 7/16 = 71/16 = 4.4375 inches = 112.7125 mm. 7 9/16 = 121/16 = 7.5625 inches = 192.0875 mm.

Each pair confirms the same relationship: multiply the whole number by the denominator and add the numerator to get the improper fraction, or divide the fraction and add the whole number to get the decimal.

Nominal lumber sizes almost always hide a mixed-number actual size. A "2x4" board measures 1 1/2" × 3 1/2" once it has been surfaced at the mill, not a true 2" × 4". Written as decimals that is 1.5" × 3.5", and in millimeters it is 38.1 mm × 88.9 mm.

Reading a tape measure adds mixed numbers constantly: two boards marked 14 5/8" and 9 3/16" need to be added before a cut list makes sense. Convert each to decimal first (14.625" and 9.1875"), add them (23.8125"), then convert back to a fraction with the decimal to fraction calculator if you need the tape-measure version again.

The most common error is forgetting to add the whole number back after converting the fraction to decimal. 2 3/4 converted incorrectly as just "0.75" throws away the 2 entirely; the correct answer is 2.75. Another frequent mistake is applying the whole number with the wrong denominator when building an improper fraction, such as writing 2 3/4 as 11/8 instead of 11/4.

Negative mixed numbers trip people up too. The negative sign applies to the whole value, not just the whole-number part, so -2 3/4 equals -(2 + 3/4) = -2.75, not -2 + 3/4. Double-check any negative conversion by verifying that the decimal falls between the two nearest negative whole numbers, in this case between -2 and -3.