What is a percent, and what is a fraction?
A percent is a fraction in a costume. The word comes from the Latin per centum — per hundred. So when you write 40%, you have already written 40/100. The conversion that textbooks make sound like a procedure is mostly just taking the costume off and tidying up what's underneath.
A fraction is two whole numbers with a line between them: a numerator on top, a denominator on the bottom. Fractions are exact in a way decimals often aren't. One third has no finite decimal — the 3s run forever — but 1/3 is an ordinary, tidy, completely precise fraction.
The two forms live in different places. Percents belong where things get compared: interest rates, test scores, discounts, poll results, tax. Fractions belong where things get divided or physically measured: a recipe, a tape measure, a sheet of plywood, a gear ratio, a probability. Nobody says "cut it by 25%" while holding a measuring cup — they say "cut it by a quarter," because 1/4 cup is a thing you can actually scoop.
40%, 2/5 and 0.4 are the same number written three ways. This page is about getting cleanly from the first to the second — in simplest form, without losing a digit on the way — and about the one case where the obvious answer is the wrong one.
How percent to fraction conversion works
Three steps, and the first one is free.
p% = p/100. Write the percent over 100, clear any decimal point by multiplying top and bottom by 10 for each decimal place, then divide both by their greatest common divisor.
Take 12.5%. Step one: write it over 100, giving 12.5/100. Step two: there's one digit after the decimal point, so multiply top and bottom by 10 — that's 125/1000. Step three: the greatest common divisor of 125 and 1000 is 125, so divide both by it. You get 1/8. As a decimal, 0.125.
40% is easier because there's nothing to clear: 40/100, GCD of 20, answer 2/5. Type either one into the percent to fraction converter and you'll see those exact intermediate numbers — the over-100 fraction, what it was multiplied by, and the GCD it was divided by — written out in a line under the result. The steps aren't hidden behind the answer, because the steps are usually what you're actually there for.
Percents over 100 become mixed numbers
Nothing changes about the method. 250% is 250/100, which reduces by 50 to 5/2. Two goes into five twice with one left over, so 5/2 is also 2 1/2 — which matches the intuition, since 250% of something is two and a half times it. Same for 150% (3/2, or 1 1/2) and 175% (7/4, or 1 3/4). Percents that are exact multiples of 100 have no fractional part at all: 100% is 1/1, 200% is 2/1, 300% is 3/1.
Why the arithmetic never touches a decimal
Under the hood the conversion reads your input digit by digit into whole-number arithmetic. It never converts your percent to a floating-point number first. That sounds fussy until you try 0.1%: as a float, 0.1 is really 0.1000000000000000055…, and a naive converter hands back a fraction with a twenty-digit numerator instead of 1/1000. Every digit you type is kept exactly, up to 15 digits before the decimal point and 18 after — which is why the percent to fraction converter holds precision well past where a pocket calculator gives up.
Common percent to fraction conversions
These are the ones worth knowing by sight. If you memorise one row, make it the eighths — they turn up constantly in recipes, tape measures and interest rates.
| Percent | Fraction | Decimal |
|---|---|---|
| 1% | 1/100 | 0.01 |
| 2% | 1/50 | 0.02 |
| 4% | 1/25 | 0.04 |
| 5% | 1/20 | 0.05 |
| 6.25% | 1/16 | 0.0625 |
| 10% | 1/10 | 0.1 |
| 12.5% | 1/8 | 0.125 |
| 15% | 3/20 | 0.15 |
| 20% | 1/5 | 0.2 |
| 25% | 1/4 | 0.25 |
| 35% | 7/20 | 0.35 |
| 37.5% | 3/8 | 0.375 |
| 40% | 2/5 | 0.4 |
| 50% | 1/2 | 0.5 |
| 60% | 3/5 | 0.6 |
| 62.5% | 5/8 | 0.625 |
| 64% | 16/25 | 0.64 |
| 75% | 3/4 | 0.75 |
| 80% | 4/5 | 0.8 |
| 87.5% | 7/8 | 0.875 |
| 90% | 9/10 | 0.9 |
| 100% | 1/1 | 1 |
| 125% | 5/4 (1 1/4) | 1.25 |
| 150% | 3/2 (1 1/2) | 1.5 |
| 250% | 5/2 (2 1/2) | 2.5 |
A pattern worth noticing: every percent in that table lands on a denominator built only from 2s and 5s — 8 is 2×2×2, 25 is 5×5, 20 is 2×2×5. That's not a coincidence. Our number system is base 10, and 10 = 2 × 5, so a fraction terminates as a decimal exactly when its reduced denominator has no other prime factors. Any other prime and the decimal runs forever, which is where the next section comes in.
Percents below 1% work identically, they just land on bigger denominators. 0.5% is 1/200, 0.1% is 1/1000, and 0.01% — a basis point, if you work anywhere near finance — is 1/10,000.
The 33.3% problem: percents that are really rounded fractions
Here is the thing most converters get wrong, and it's the reason this one exists in the shape it does.
Ask for 33.3% as a fraction and the honest, literal answer is 333/1000. Those digits say what they say, and 333/1000 doesn't reduce — 333 and 1000 share no common factor. But almost nobody typing 33.3% wants 333/1000. They split something three ways, saw 33.3% on a screen, and want 1/3 back.
So the percent to fraction converter gives you both. The main result card shows the exact fraction your digits describe. Underneath, when your digits look like a repeating decimal that got rounded or cut off, a second line appears: Meant 33.3333…% repeating? That's exactly 1/3.
| You type | Exactly | Probably meant |
|---|---|---|
| 33.3% | 333/1000 | 1/3 |
| 66.7% | 667/1000 | 2/3 |
| 11.1% | 111/1000 | 1/9 |
| 22.2% | 111/500 | 2/9 |
| 16.67% | 1667/10000 | 1/6 |
| 83.33% | 8333/10000 | 5/6 |
| 8.33% | 833/10000 | 1/12 |
| 41.67% | 4167/10000 | 5/12 |
Which one should you use? If the number genuinely stops where you typed it — a measured lab result, a price, a reading off an instrument — use the exact fraction. If it came from dividing something into equal parts, use the repeating one. The gap matters more than it looks: split a $300 bill three ways and each share is $100, but 33% of $300 is $99, leaving a dollar nobody paid.
The suggestion only appears when your digits actually reach into the repeat. A flat 33% stays 33/100, because 33% is genuinely just 33/100 and guessing otherwise would be presumptuous. Type 33.3% and the note shows up.
When you'll need to convert a percent to a fraction
Homework is the obvious one, and worksheets almost always want lowest terms rather than 50/100. Beyond that, the conversion earns its keep in a few ordinary places.
Scaling a recipe. A recipe scaled to 150% is a recipe times 3/2 — and 3/2 is something you can do with measuring cups, where 150% is not. Same logic going down: 75% of a cup is 3/4 of a cup.
Reading a discount as a ratio. 40% off means you pay 60%, which is 3/5 of the sticker price. Once it's a fraction the mental arithmetic gets easier: 3/5 of $45 is three lots of $9.
Measuring things in the physical world. Tape measures, drill bits, wrench sets and lumber are all sold in eighths and sixteenths. A spec given as 87.5% is 7/8, and 7/8 is a line printed on the tape.
Probability and odds. A 20% chance is 1/5, which reads as "one in five" — closer to how people actually reason about risk.
Filling in a form that only takes fractions. Some forms, especially legal and property ones, insist on fractional ownership shares. A 12.5% stake has to go in as 1/8.
Edge cases and gotchas
A few things that surprise people, and what to do about each.
Negative percents are fine. −40% comes back as −2/5, with the sign on the numerator where convention puts it. A fraction is never written with a negative denominator.
Zero has a fraction too. 0% is 0/1. There's nothing to reduce, and the converter says so rather than showing you 0/100.
Typing a fraction gets you an error, not an answer. This converter reads percents. Enter 1/7 and it will tell you it can't read that — you want the fraction to decimal converter for the trip in that direction.
Commas work both ways. 1,250% is read as twelve-hundred-and-fifty percent (25/2, or 12 1/2), while 12,5% is read as twelve-point-five in the European style (1/8). The rule is that whichever separator comes last is the decimal point.
Rare repeating fractions need more digits. The repeat-detection looks for denominators up to 1000, but it also waits until your digits show the pattern twice. Sevenths repeat in six-digit cycles, so 14.2857% is not enough for the converter to offer 1/7 — it returns the literal 142857/1000000. Type 14.28571% and 1/7 appears. That's a deliberate trade: guessing from too few digits would mean guessing wrong.
There are limits, and they're stated. Up to 15 digits before the decimal point, 18 after, 64 characters total. Past any of those you get a message naming the limit you hit, rather than a quietly rounded answer. The % sign is optional, and so are trailing ellipses, the word "percent", a leading dot (.5), and scientific notation (1.5e-3%).
Related fraction and percentage tools
Going the other way, or arriving from a different starting point, there's a tool for each leg of the trip. Start from a decimal instead of a percent with the decimal to fraction converter, which shares the same parser, so "0,75" and "1.5e-3" behave identically on both pages. Turn a fraction back into a decimal with the fraction to decimal converter. If you already have a fraction and just want it in lowest terms, the fraction simplifier does that one job. For adding, subtracting or multiplying fractions once you have them, use the fraction calculator. And for the percentage arithmetic itself — what's 15% of 80, what percent is 12 of 48 — there's the percentage calculator and the percent change calculator.
Each of those is its own page that does its own single job. That's the whole idea. The usual shape of software like this is a calculator buried three clicks inside a suite you pay monthly for, or a one-line answer sitting behind a 14-day trial, an email address and a payment method on file. A percent to fraction converter is not a subscription-shaped problem. It's a box you type into. Open it, get the fraction, close the tab — no account, no trial, nothing to cancel later. Microapp pays for itself through an annual membership and gives 10% of every dollar it earns to charity, off the top, audited quarterly. This converter costs nothing and is the full tool, not a preview of one.
Frequently asked questions
What is 12.5% as a fraction?
1/8. Start with 12.5/100, multiply top and bottom by 10 to clear the decimal point — that's 125/1000 — then divide both by their GCD of 125. The eighths are the family worth memorising: 12.5% = 1/8, 25% = 1/4, 37.5% = 3/8, 50% = 1/2, 62.5% = 5/8, 75% = 3/4, 87.5% = 7/8.
What is 33.3% as a fraction?
Exactly, 33.3% is 333/1000 — that's what those digits say, and it doesn't reduce. But 33.3% is usually 1/3 written down with the decimal cut short, since 1/3 is 33.3333…% with the 3s going on forever. The converter shows the exact 333/1000 in the main card and notes 1/3 underneath. Use 333/1000 if the number really stops there; use 1/3 if it came from splitting something three ways.
How do you convert a percent to a fraction by hand?
Write the percent over 100, clear any decimal point, then reduce. "Percent" means per hundred, so 40% is literally 40/100 — half the work is done before you start. Find the greatest common divisor of top and bottom and divide both by it; for 40 and 100 that's 20, leaving 2/5. If there's a decimal point, multiply top and bottom by 10 for each decimal place first.
How do I turn a percent over 100 into a mixed number?
Convert it the normal way, then pull out the whole part. 250% is 250/100, which reduces by 50 to 5/2. Two goes into five twice with one left over, so 5/2 is 2 1/2. The percent to fraction converter shows the mixed number automatically whenever the percent is above 100 and doesn't land on a whole number.
Can I enter a negative percent, or one smaller than 1%?
Both work. −40% returns −2/5, sign on the numerator. Small percents just produce larger denominators: 0.5% is 1/200, 0.1% is 1/1000, 0.01% is 1/10,000. These are ordinary quantities in interest rates and error margins, and because the arithmetic runs on whole numbers rather than floating point, the precision holds all the way down to 18 decimal places.
Is what I type saved or sent anywhere?
No. The conversion runs entirely in your browser. Nothing is sent to a server, nothing is stored, and closing the tab clears it.