CalConverters

Percent to Fraction Calculator

Convert any percent to a simplified fraction with a five-step working — including decimal percents like 12.5% and improper percents like 150%.

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How to use this calculator

Type a percent value into the input — no % sign needed; the calculator handles whole numbers (23), decimals (12.5), and percents greater than 100 (150). Negative values like -25 work too.

The result shows the simplified fraction at the top, with the step-by-step breakdown underneath so you can follow each operation. If the answer is improper (≥\ge 100%), it also shows the mixed-number form.

Tip: The fraction shown is always in lowest terms. To see the unreduced fraction, watch step 3 of the breakdown — that's the percent rewritten as a whole-numerator fraction before the GCD reduction.

How to convert a percent to a fraction — the formula

Every percent-to-fraction conversion follows the same five-step recipe:

  1. Write the percent over 100. 23% = 23/100. By definition, that's what "percent" means.
  2. Move the decimal point two places left to get the decimal form. 23/100 = 0.23. (This step is mostly for understanding — the math works without it.)
  3. Multiply numerator and denominator by 10n10^n where n = the number of decimal places. This clears any decimal in the numerator. 0.23 × 100/100 = 23/100.
  4. Reduce by the GCD (greatest common divisor) to put the fraction in lowest terms.
  5. Convert to a mixed number if the simplified fraction is improper (numerator ≥\ge denominator > 1).

For whole-number percents (like 23%, 75%, 150%) the decimal step is trivial — the fraction percent/100 is already integer-over-integer, so you skip straight to step 4 (reduce by GCD).

For decimal percents (like 12.5%, 0.5%, 0.07%) the multiply-by-10n10^n step is what makes the math exact. Don't divide using a calculator and convert the decimal — floating-point rounding will make 0.07/100 × 10000 come out as 7.000000000000001, not 7. This calculator uses big-integer arithmetic so the result is always exact.

Tip: If your percent has n digits after the decimal point, the simplified fraction will have a denominator that's a divisor of 100×10n100 \times 10^n. So 0.07% (two decimal places) gives a denominator that divides 10,000 — and the answer turns out to be 710000\frac{7}{10000}.

Worked examples

Example 1 — 75%

  1. 75% = 75/100 = 0.75
  2. = 0.75/1
  3. = 0.75/1 × 100/100 = 75/100
  4. gcd⁡(75,100)=25\gcd(75, 100) = 25. 75/100 ÷ 25 = 3/4
  5. 3/4 is proper. Answer: 34\frac{3}{4}

Example 2 — 12.5%

  1. 12.5% = 12.5/100 = 0.125
  2. = 0.125/1
  3. = 0.125/1 × 1000/1000 = 125/1000
  4. gcd⁡(125,1000)=125\gcd(125, 1000) = 125. 125/1000 ÷ 125 = 1/8
  5. 1/8 is proper. Answer: 18\frac{1}{8}

Example 3 — 150%

  1. 150% = 150/100 = 1.5
  2. = 1.5/1
  3. = 1.5/1 × 10/10 = 15/10
  4. gcd⁡(15,10)=5\gcd(15, 10) = 5. 15/10 ÷ 5 = 3/2
  5. 3/2 is improper. As a mixed number: 3 ÷ 2 = 1 remainder 1 → 1121\frac{1}{2}. Answer: 32=112\frac{3}{2} = 1\frac{1}{2}

Example 4 — 0.5%

  1. 0.5% = 0.5/100 = 0.005
  2. = 0.005/1
  3. = 0.005/1 × 1000/1000 = 5/1000
  4. gcd⁡(5,1000)=5\gcd(5, 1000) = 5. 5/1000 ÷ 5 = 1/200
  5. 1/200 is proper. Answer: 1200\frac{1}{200}

Common percents reference

PercentFractionMixed (if improper)
1%1100\frac{1}{100}—
5%120\frac{1}{20}—
10%110\frac{1}{10}—
12.5%18\frac{1}{8}—
20%15\frac{1}{5}—
25%14\frac{1}{4}—
33.33%333310000\frac{3333}{10000}—
37.5%38\frac{3}{8}—
50%12\frac{1}{2}—
62.5%58\frac{5}{8}—
66.67%666710000\frac{6667}{10000}—
75%34\frac{3}{4}—
87.5%78\frac{7}{8}—
100%1—
125%54\frac{5}{4}1141\frac{1}{4}
150%32\frac{3}{2}1121\frac{1}{2}
200%2—
250%52\frac{5}{2}2122\frac{1}{2}
300%3—

Precision note

This calculator treats your input as typed. Type 33.33% and you get 3333/10000, not 1/3 — because 33.33% is not exactly one-third. If you want the exact 13\frac{1}{3}, type the repeating-decimal value, or use the fraction-to-percent calculator in reverse to see that 13=33.3‾%=33.333…%\frac{1}{3} = 33.\overline{3}\% = 33.333\ldots\%.

The underlying arithmetic uses arbitrary-precision integers (BigInt), so there is no precision loss — 0.07% → 7/10000 is exact, not a rounded approximation. The same code handles 1e-9% (one billionth of a percent) just as cleanly.

Frequently asked questions

How do you convert a percent to a fraction?
Five steps: write the percent over 100, drop the % sign, multiply numerator and denominator by 10 for each decimal place in the percent so the numerator is a whole number, reduce by the GCD, then convert to a mixed number if the result is improper. 75% becomes 75100\frac{75}{100}, which reduces to 34\frac{3}{4}.
What is 12.5% as a fraction?
12.5% = 18\frac{1}{8}. Walk through it: 12.5100=0.125\frac{12.5}{100} = 0.125. Multiply top and bottom by 1000 to clear the decimal: 1251000\frac{125}{1000}. Divide both by 125 (the GCD): 18\frac{1}{8}. So 12.5% and 18\frac{1}{8} are exactly equal.
What is 75% as a fraction in simplest form?
75% = 34\frac{3}{4}. Start with 75100\frac{75}{100}. The greatest common divisor of 75 and 100 is 25, so divide both by 25: 75÷25=375 \div 25 = 3, 100÷25=4100 \div 25 = 4. The simplified fraction is 34\frac{3}{4}.
How do you convert a percent greater than 100% to a fraction?
Use the same steps — 150% becomes 32\frac{3}{2} after reducing by 50. Because 32\frac{3}{2} is an improper fraction (numerator larger than denominator), you can also write it as the mixed number 1121\frac{1}{2}. Both forms are exactly the same value.
What is 33.33% as a fraction? Is it 1/3?
33.33% is not exactly 13\frac{1}{3} — this calculator treats the input as written. 33.33% = 333310000\frac{3333}{10000} (already in lowest terms). To get 13\frac{1}{3} you'd need the exact repeating decimal 33.333…%. Choose your input precision based on whether you mean the literal typed value or the conceptual fraction.
What is 0.5% as a fraction?
0.5% = 1200\frac{1}{200}. Steps: 0.5100=0.005\frac{0.5}{100} = 0.005. Multiply top and bottom by 1000 to clear decimals: 51000\frac{5}{1000}. gcd⁡(5,1000)=5\gcd(5, 1000) = 5, so divide both: 1200\frac{1}{200}. Note how small percents create large denominators.
Why divide by 100 to convert a percent to a fraction?
Percent literally means "per hundred" — Latin per centum. So 23% is shorthand for 23 per 100, or 23100\frac{23}{100}. Every percent-to-fraction conversion starts from that definition. The rest is just simplifying.
Can a negative percent be converted to a fraction?
Yes — the sign carries straight through. −25%-25\% becomes −25100=−14\frac{-25}{100} = \frac{-1}{4}. The minus sign attaches to the numerator (or to the whole number if the result is a mixed number), never to the denominator.

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