Fraction / Decimal / Percent Converter
Convert between fractions, decimals, and percentages in any direction. Six conversion modes in one tool.
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How to use this calculator
- 1
Select the conversion direction from the dropdown.
- 2
Enter the numerator (or decimal/percent value) in the first field.
- 3
For fraction modes, also enter the denominator.
- 4
The converted value is shown immediately, along with all three forms (fraction, decimal, percent).
Frequently asked questions
Which fields do I use for each conversion?
In the fraction modes, enter the numerator in the first box and the denominator in the second. In the decimal and percent modes only the first box is used and the denominator is ignored. In every mode the output also shows the other two representations, so a fraction-to-percent run also reports the decimal.
Why does 0.333333 become 333333/1000000 instead of 1/3?
Decimal-to-fraction conversion rounds the number to nine decimal places and reduces the resulting fraction. It does not detect repeating patterns, so a truncated 0.3333 is treated as exactly 3333/10000. For a repeating value, convert from the fraction instead: 1/3 in fraction-to-percent mode gives 33.333333%.
Does the fraction in the output get simplified?
Only in the modes that create a fraction from a decimal or percent. 0.375 returns 3/8 and 62.5% returns 5/8. In the fraction modes the fraction is echoed as typed, so 6/8 stays 6/8 even though the percent is 75%. Use a fraction simplifier if you need lowest terms.
Can the percentage exceed 100 or be negative?
Yes. An improper fraction such as 9/4 returns 225% and a decimal of 2.25. A negative numerator or denominator gives a negative percent: 3 over −4 returns −75%, though the fraction is displayed as typed, 3/−4.
What happens when the denominator is 0?
In the two fraction modes the calculator shows an error that the denominator cannot be zero. A fraction with a zero denominator has no value, so no percent or decimal is produced.
How many decimal places are shown?
Up to six, with trailing zeros removed. That is why 1/3 appears as 0.333333 and 33.333333%. The underlying value is more precise, but the display is rounded.
How do the percent and decimal modes differ from fractions?
A percent is a decimal multiplied by 100, so 7.5% is 0.075 and 0.045 is 4.5%. Those two modes are simple shifts of the decimal point with no fraction involved. Mixed numbers like 1 1/2 are not accepted directly; convert to an improper fraction (3/2) first.
Fraction, decimal and percent converter — six directions, one tool
How the three forms relate
A fraction, a decimal and a percent are three ways to write one quantity. The decimal is the numerator divided by the denominator. The percent is the decimal times 100. Going the other way, a percent divided by 100 is a decimal, and a decimal can be written as a fraction over a power of ten and then reduced.
| Fraction | Decimal | Percent |
|---|---|---|
| 3/4 | 0.75 | 75% |
| 7/8 | 0.875 | 87.5% |
| 5/16 | 0.3125 | 31.25% |
| 3/8 | 0.375 | 37.5% |
| 5/8 | 0.625 | 62.5% |
| 1/8 | 0.125 | 12.5% |
| 9/4 | 2.25 | 225% |
Worked example: a test score
A student answers 7 of 8 questions correctly. In fraction-to-percent mode, 7 over 8 gives 87.5% and a decimal of 0.875. For a score of 5 out of 16, fraction-to-decimal gives 0.3125 and 31.25%. The percent line is the one most graders report, but the decimal is what you multiply by if you want to scale another quantity.
Worked example: starting from a decimal or percent
The decimal 0.375 converts to the fraction 3/8, or 37.5%. A percent of 62.5% converts to the fraction 5/8 and a decimal of 0.625. A percent of 12.5% is 1/8. Percent to decimal for 7.5% returns 0.075, and decimal to percent for 0.045 returns 4.5%. The fraction is reduced to lowest terms in these modes.
Repeating decimals and rounding
Fractions like 1/3 have decimals that never end, so any displayed decimal is rounded. In fraction mode 1/3 shows as 0.333333, or 33.333333%. Going back from the decimal is not exact: entering 0.333333 yields 333333/1000000, because the converter works from the digits you typed rather than guessing a pattern. If a result matters, work from the original fraction.
Improper fractions and negatives
Values above 1 simply give percentages above 100, and 9/4 reports as 225%. Negative inputs carry their sign through the percentage. The converter does not build mixed numbers, so rewrite 2 1/4 as 9/4 before entering it. The denominator must be non-zero in the fraction modes. A percent field accepts decimals as well, so 12.5 means 12.5%, and typing 0.5 in percent mode means one half of one percent, which is 0.005 as a decimal.
Learn more from an authoritative source:
WikipediaDecimal to Fraction Calculator
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Compare and order up to four fractions from smallest to largest, showing decimal equivalents and the LCD. Leave unused fields at 0.
Equivalent Fractions Calculator
Generate a list of equivalent fractions for any given fraction. Shows the simplified form and up to 10 equivalents.
LCD — Least Common Denominator
Find the Least Common Denominator (LCD) of up to four denominators, with prime factorization method shown step-by-step.
Long Division Calculator
Divide any two integers with step-by-step long division. Shows quotient, remainder, decimal result, and the full long division process as text.
Results are estimates for informational purposes only and do not constitute professional financial, medical, legal, or technical advice. Read full disclaimer →