acalculator

How to change fraction to percent?

Type a fraction or mixed number. The fraction to percent calculator divides it out, multiplies by 100, and shows the exact percent or a rounded one, with the working.

Your numbers

Type 5/8, or 1 3/4 for a mixed number.
Percent
62.5%

5/8 = 5 ÷ 8 = 0.625; 0.625 × 100 = 62.5%.

Rounded percent
62.50%
Decimal
0.625
Exact?
yes
How
5/8 = 5 ÷ 8 = 0.625; 0.625 × 100 = 62.5%

Percent: 62.5%. 5/8 = 5 ÷ 8 = 0.625; 0.625 × 100 = 62.5%.

How to calculate

Turns a fraction or mixed number into a percent: the exact percent when its decimal ends (5/8 is 62.5%), or rounded to the places you pick (1/3 is about 33.33%).

Example with the default inputs (Fraction 5/8, Round to (decimal places) 2): 5/8 = 5 ÷ 8 = 0.625; 0.625 × 100 = 62.5%.

Method: percent = numerator ÷ denominator × 100. The decimal ends when the denominator in lowest terms has no prime factor other than 2 and 5; then the percent is exact. Otherwise it is rounded, halves away from zero.

  • The fraction is reduced to lowest terms first; all arithmetic is exact.
  • A rounded percent keeps exactly the chosen number of decimal places; halves round away from zero.

Machine-readable copies: Markdown, JSON.

Worked examples

Each example is checked against the calculator on every build.

  1. Fraction 5/8, Round to (decimal places) 2 gives Percent 62.5%, Rounded percent 62.50%, Decimal 0.625, Exact? yes, How 5/8 = 5 ÷ 8 = 0.625; 0.625 × 100 = 62.5%.Source: OpenStax, Prealgebra 2e, §6.1 Understand Percent (convert a fraction to a percent: write it as a decimal, then multiply by 100), https://openstax.org/books/prealgebra-2e/pages/6-1-understand-percent (retrieved 2026-10-05)
  2. Fraction 1/3, Round to (decimal places) 2 gives Percent ≈ 33.33%, Decimal 0.3333, Exact? no, the decimal repeats.Source: OpenStax, Prealgebra 2e, §6.1 Understand Percent (convert a fraction to a percent: write it as a decimal, then multiply by 100), https://openstax.org/books/prealgebra-2e/pages/6-1-understand-percent (retrieved 2026-10-05)
  3. Fraction 2/3, Round to (decimal places) 1 gives Percent ≈ 66.7%, Rounded percent 66.7%.Source: OpenStax, Prealgebra 2e, §6.1 Understand Percent (convert a fraction to a percent: write it as a decimal, then multiply by 100), https://openstax.org/books/prealgebra-2e/pages/6-1-understand-percent (retrieved 2026-10-05)
  4. Fraction 1 3/4, Round to (decimal places) 0 gives Percent 175%, Rounded percent 175%, Decimal 1.75.Source: OpenStax, Prealgebra 2e, §6.1 Understand Percent (convert a fraction to a percent: write it as a decimal, then multiply by 100), https://openstax.org/books/prealgebra-2e/pages/6-1-understand-percent (retrieved 2026-10-05)
  5. Fraction -1/8, Round to (decimal places) 1 gives Percent −12.5%, Rounded percent −12.5%, Decimal −0.125.Source: OpenStax, Prealgebra 2e, §6.1 Understand Percent (convert a fraction to a percent: write it as a decimal, then multiply by 100), https://openstax.org/books/prealgebra-2e/pages/6-1-understand-percent (retrieved 2026-10-05)
  6. Fraction 1/16, Round to (decimal places) 0 gives Percent 6.25%, Rounded percent 6%.Source: OpenStax, Prealgebra 2e, §6.1 Understand Percent (convert a fraction to a percent: write it as a decimal, then multiply by 100), https://openstax.org/books/prealgebra-2e/pages/6-1-understand-percent (retrieved 2026-10-05)

How it works

percent = numerator ÷ denominator × 100

  1. The fraction (or mixed number: w a/b = (w × b + a)/b, with the sign on the whole) is reduced to lowest terms.
  2. Does the decimal end? It ends exactly when the denominator in lowest terms has no prime factor other than 2 and 5. Then it has k decimal places, where k is the larger of the number of 2s and the number of 5s in the denominator.
  3. Percent. When the decimal ends, the percent is exact: the decimal × 100, written with k − 2 decimal places (at least 0). When it repeats, the headline shows ≈ and the rounded percent.
  4. Rounded percent. The percent rounded to the chosen number of decimal places (0 to 10, default 2), keeping trailing zeros, with a half rounded away from zero.
  5. Decimal. The exact decimal when it ends; otherwise the decimal rounded to 2 more places than the percent.

All arithmetic is exact. Negative values show a true minus sign (−).

Output format. The "How" line reads <fraction> = <num> ÷ <den> = <decimal>; <decimal> × 100 = <percent>%, with ≈ in place of = when the decimal repeats. The fraction is shown in lowest terms as an improper fraction.

Worked examples by hand

5/8. 5 ÷ 8 = 0.625; 0.625 × 100 = 62.5% (exact). Rounded to 2 places: 62.50%.

1/3, 2 places. 1 ÷ 3 = 0.3333…; × 100 = 33.333…% ≈ 33.33%.

2/3, 1 place. 66.666…% ≈ 66.7%.

1 3/4. 7/4 = 1.75; × 100 = 175%.

−1/8, 1 place. −0.125 × 100 = −12.5%.

1/16, 0 places. 1 ÷ 16 = 0.0625 = 6.25%, rounded to 6%.

Other questions people ask

How do you change a fraction to a percent?

Divide the top by the bottom, then multiply by 100. 5/8 = 5 ÷ 8 = 0.625, and 0.625 × 100 = 62.5%.

What is 1/3 as a percent?

1 ÷ 3 = 0.333…, so 1/3 is 33.333…%, about 33.33% to two decimal places. The 3s never end.

When is the percent exact?

When the bottom number, in lowest terms, has no prime factors other than 2 and 5 (such as 4, 8, 20 or 25). Then the decimal ends. Any other factor, such as 3 or 7, gives a repeating decimal.

How do I convert a mixed number?

Write it as an improper fraction first: 1 3/4 = 7/4 = 1.75 = 175%. A fraction above 1 is more than 100%.

Is there a shortcut for fractions over 100?

Yes: a fraction over 100 is already a percent. 37/100 is 37%. For 3/20 you can also scale the bottom to 100: 3/20 = 15/100 = 15%.

How does the page round?

It keeps the number of decimal places you choose and rounds a half away from zero: 66.666…% to one place is 66.7%.