Fraction to Percent Calculator

What the converter returns

A percent is a fraction with 100 on the bottom. That is the whole idea, and it explains both directions of the conversion: to go from a fraction to a percent, work out the fraction as a decimal and multiply by 100. To go back, divide the percent by 100 and reduce.

Enter the numerator and the denominator, and add a whole number if you have a mixed number. The page returns the percent at the rounding you pick, the exact percent before rounding, the decimal value, the fraction in lowest terms, and the same percent written as a count out of 100. A second box takes a percent and returns the fraction.

The rounding choice is not cosmetic. One third is 33.3333 percent and never ends, so any printed answer is a decision about how much of it to keep. Two decimals is the usual choice for survey and test results, one decimal is common for rates and price changes, and whole numbers are what most school gradebooks and nutrition labels use.

The page does not round twice. It computes from the original fraction each time, so the two decimal, one decimal and whole number answers all come from the same exact value rather than from each other.

The one step that turns a fraction into a percent

Divide the numerator by the denominator, then multiply by 100. For three eighths that is 3 divided by 8, which is 0.375, times 100, which is 37.5. Written as one line, percent = numerator / denominator x 100.

Twenty five cents out of a dollar is the model to keep in mind, because a dollar is 100 cents. Twenty five cents is 25 percent of a dollar, and 1/4 of a dollar is 25 cents, so 1/4 is 25 percent. The same logic sizes any fraction against a hundred.

Two more examples, one that comes out clean and one that does not. A test with 45 correct answers out of 50 is 45 / 50 = 0.9, which is 90 percent. A recipe that uses 5 parts out of 12 is 5 / 12 = 0.41666 and so on, which is 41.67 percent at two decimals. The first answer is exact, the second is a rounding, and both come from the same division.

The direction matters. Dividing the wrong way gives 12 / 5 = 2.4, which is 240 percent, and that answer is only right if you meant the ratio of the whole to the part rather than the part to the whole.

Fractions worth memorizing as percents

Most conversions in daily life come from a short list, and knowing the list removes the need for a calculator. Halves, quarters and eighths are exact: 1/2 is 50, 1/4 is 25, 3/4 is 75, 1/8 is 12.5, 3/8 is 37.5, 5/8 is 62.5, 7/8 is 87.5. Thirds and sixths repeat: 1/3 is 33.33, 2/3 is 66.67, 1/6 is 16.67, 5/6 is 83.33.

The list also gives you estimates for fractions that are not on it. Five twelfths sits between one third and one half, so it is between 33.33 and 50 percent, and the exact answer of 41.67 is close to the middle. Seven sixteenths sits between 3/8 and 1/2, which puts it between 37.5 and 50, and the exact answer is 43.75.

That trick is how people compare fractions quickly on a menu, a discount sign or a report. The exact number is one division away, and the rough position tells you whether the division answer is plausible before you trust it.

Rounding decides the answer you print

Rounding a repeating percent is where two correct calculations can give different printed answers. The table shows the same values at three levels of precision.

Read the whole number column carefully. One eighth is 12.5 percent, and rounding to the nearest whole number gives 13, not 12, because the standard rule sends a tie upward. One third rounds to 33 while two thirds rounds to 67, so a table of whole number percents can add up to more than 100 if the values came from rounding separate fractions.

Two rules avoid most of the trouble. Round only once, at the end, never in the middle of a calculation. And state the precision when the number matters: 33.33 percent is not the same as one third, it is smaller by 0.0033 of a percentage point, which on a population of 300 million people is about 10,000 people.

Some published numbers have their own rules. The Food and Drug Administration's Daily Value page works the percent out as a fraction of a reference amount, so 30 micrograms of a nutrient against a 300 microgram Daily Value is 10 percent, and the label prints a whole number rather than 10.0. The rounding is part of the labelling rule, not part of the fraction.

Percentage points are not percent

Two fractions that look close can move a number by a lot, and the difference between a percentage point and a percent is where arguments start. Going from 1/4 to 3/8 takes the share from 25 percent to 37.5 percent.

That is a rise of 12.5 percentage points. It is also a rise of 50 percent, because 37.5 / 25 = 1.5. Both statements describe the same change, and a headline that says the cost rose 12.5 percent when it rose 12.5 points understates the change by a factor of four.

The same trap sits in any comparison of fractions. Two thirds against one half is 66.67 against 50, which is 16.67 points and a rise of 33.33 percent. One eighth against one sixth is 12.5 against 16.67, which is a fall of about 4.17 points, or about 25 percent of the earlier value.

When you report a change, name the unit. Percentage points for the gap between two percentages, percent for the relative size of the move. Surveys, election results and interest rate changes all live in this distinction, and the wrong unit is the single commonest error in a summary paragraph.

Scores, discounts, tips and rates

Four everyday uses, each with the arithmetic spelled out.

Test scores. A score of 84 out of 96 is 84 / 96 = 0.875, which is 87.5 percent. A score of 33 out of 40 is 82.5 percent. If the grader rounds to whole numbers, 87.5 becomes 88 and 82.5 becomes 83. Whether a test rounds at all is set by the grading policy, not by the fraction.

Discounts. One third off a 60 dollar item is 60 x 1/3 = 20 dollars off, leaving 40 dollars. Using 33 percent instead gives 19.80 dollars off and a 40.20 dollar price, which is 20 cents more than the exact third. On small amounts that gap is noise, and on a 3,000 dollar order it is 10 dollars.

Tips. One sixth of an 84 dollar check is 14 dollars, which is 16.67 percent. Reading the tip off the fraction is faster than punching percentages into a phone, and it lands in the range most people mean by a normal tip.

Rates quoted as fractions. A mortgage rate of 5 5/8 percent is 5.625 percent, not 5.5 and not 5.8. The fraction is part of the rate, and dropping it changes a payment by real money over 30 years. The same care applies to a 3/8 percent fee, which is 0.375 percent, or 0.00375 as a decimal.

Turning a percent back into a fraction

Divide by 100 and reduce. That is the full method, and the only subtlety is how many digits the percent carried.

A percent with one decimal place becomes a fraction over 1000. Thirty seven and a half percent is 37.5 / 100 = 375 / 1000, and dividing both by 125 gives 3/8. A percent with two decimal places becomes a fraction over 10,000, which is why 33.33 percent is 3333/10000 rather than 1/3.

That last point is the one worth carrying away. A rounded percent cannot come back to the original fraction unless the fraction had a denominator that divides the power of ten you are using. One eighth does, because 1000 is divisible by 8. One third does not, because no power of ten is divisible by 3. If you need the exact fraction, keep the fraction.

The check runs both ways: whatever fraction the page returns, dividing it out and multiplying by 100 should give back the percent you typed, and the page shows that value alongside the fraction so the two can be compared at a glance.

Where the answer goes wrong

Five mistakes account for most of the bad conversions people bring to this page.

Forgetting the multiply by 100. Three eighths is 0.375 as a decimal and 37.5 as a percent. Writing 0.375 percent shrinks the value by a factor of 100, and it is the error that shows up most often in drafts and slide decks.

Reading 3/8 as 3.8. The slash is division, not a decimal point. The two numbers are not digits of one decimal, and 3/8 is 0.375 while 3.8 is nineteen times larger.

Dividing the wrong way. Part over whole gives the share. Whole over part gives something else entirely, which is why 8/3 comes out at 266.67 percent.

Rounding twice. Converting 1/3 to 0.33 and then to 33 percent loses a third of a percentage point against the correct 33.33 percent. Keep the exact value until the last step.

Treating a percent of a percent as a plain percent. A 20 percent discount followed by another 20 percent discount is not 40 percent off. It is 1 - (0.8 x 0.8) = 0.36, which is 36 percent off, and the difference grows with each additional discount. Public reporting follows the same habit of quoting shares as percentages: the NAEP mathematics assessment reports results as the percentage of students at each achievement level, and those percentages are rounded shares of a sample rather than exact counts of every student in the country.