Ratio to Fraction Calculator: Convert Ratios to Fractions

How the ratio becomes a fraction

A ratio a:b is a comparison of two parts, and the fraction a/b is the first part measured against the second. The conversion is one division: 3:4 is 3 divided by 4, which is 0.75, which is 75%. The part-to-whole shares need one more step: add the parts to get the whole — 3 + 4 = 7 — and divide each part by the whole. The 3 parts are 3/7 of the whole, which is about 42.86%, and the 4 parts are 4/7, which is about 57.14%. The two shares always add to 100%: 42.86% plus 57.14% is 100%. And if the ratio can be simplified, simplify it first: divide both parts by their greatest common divisor. 6:8 divides by 2 to give 3:4, so 6:8 is 3/4 as well — the same fraction, the same decimal, the same percent.

The worked examples, line by line

3:4 is 3/4: 3 divided by 4 = 0.75 = 75%. The whole is 7 parts: 3/7 is about 42.86% and 4/7 is about 57.14%.

1:2 is 1/2: 1 divided by 2 = 0.50 = 50%. The whole is 3 parts: 1/3 is about 33.33% and 2/3 is about 66.67%.

5:3 is 5/3: 5 divided by 3 = 1.6667 (rounded to four decimals) = 166.67%. A ratio over 1:1 gives a fraction over 1, because the first part is bigger than the second.

2:5 is 2/5: 2 divided by 5 = 0.40 = 40%. The whole is 7 parts: 2/7 is about 28.57% and 5/7 is about 71.43%.

6:8 simplifies to 3:4: the greatest common divisor of 6 and 8 is 2, so 6 divided by 2 is 3 and 8 divided by 2 is 4 — 3:4 — which is 3/4 = 0.75 = 75%, the same as the default.

Reverse mode: decimals back into ratios

Reverse mode turns a decimal into the nearest simple ratio, with a denominator up to 100. 0.75 is 3:4 — exact, because 3 divided by 4 is exactly 0.75. 0.333 is about 1:3 — approximate, because 1 divided by 3 is 0.3333…, which never ends, so no finite decimal is exactly one third; 1:3 is the nearest simple ratio, and the calculator says so. 2.5 is 5:2 — exact, because 5 divided by 2 is 2.5. 0.2 is 1:5 — exact, because 1 divided by 5 is 0.2. The rule the calculator follows is to find the ratio with the smallest denominator that gets closest to the decimal, and to say plainly whether the match is exact or only approximate — a repeating decimal like 0.333 can never be exact, and pretending otherwise would be wrong.

Part-to-part vs part-to-whole: the one mistake to avoid

The one mistake people make with ratios is reading 3:4 as 3 out of 4. It is not: 3:4 means 3 parts to 4 parts, and the whole is 7 parts, so 3 parts is 3/7 of the whole — about 42.86% — not 3/4. The fraction 3/4 is the first part measured against the second part, not against the whole. The two readings answer different questions: 3/4 answers "how big is the first part compared with the second?", and 3/7 answers "how big is the first part compared with everything?". A recipe that calls for flour and sugar in the ratio 3:4 is 3 parts flour to 4 parts sugar, and flour is 3/7 of the mix. A class with boys and girls in the ratio 1:2 has 1/3 boys and 2/3 girls, not 1/2 boys. Keep the two straight and the numbers stop surprising you.

Rounding convention, stated plainly: decimals are shown to four places and percents to two, and the yearly-style totals are the unrounded values rounded at the end — so 3/7 shows as 42.86% (the exact figure is 42.8571…%) and 1/3 shows as 33.33% (the exact figure is 33.3333…%). The ratio itself is exact: 6:8 simplifies to exactly 3:4, and 0.75 is exactly 3:4.

Output · formula · meaning

Who uses this

• The student checking homework: has the ratio 3:4 and learns it is 3/4 = 0.75 = 75% — with the part-to-whole shares 42.86% and 57.14% showing why 3:4 is not 3 out of 4.
• The cook scaling a recipe: has flour and sugar in the ratio 1:2 and learns the mix is 1/3 flour and 2/3 sugar — 33.33% and 66.67% — so doubling the recipe keeps the shares the same.
• The teacher explaining ratios: shows a class that 6:8 simplifies to 3:4 — divide both parts by 2 — and that both are 3/4 = 0.75 = 75%, the same fraction in two costumes.
• The decimal converter: has 0.333 and learns it is about 1:3 — and that the calculator says approximate, because 1/3 is 0.3333… and no finite decimal is ever exactly one third.

Accuracy & limitations

The conversion is exact: a ratio a:b is a/b by definition, and the decimal and the percent are that division carried out — 3:4 is exactly 0.75 and exactly 75%. The simplification is exact too: dividing both parts by their greatest common divisor gives the same ratio in lowest terms. The only place approximation enters is the display: decimals are shown to four places and percents to two, so 3/7 shows as 42.86% when the exact figure is 42.8571…%, and 1/3 shows as 33.33% when the exact figure is 33.3333…%. Reverse mode is approximate by design: it finds the nearest simple ratio with a denominator up to 100, and it says plainly whether the match is exact — 0.75 is exactly 3:4 — or only approximate — 0.333 is about 1:3, because 1/3 never ends. The calculator rejects zero, negative, and empty inputs, and ratio parts above 100,000: a ratio with a zero part is not a ratio, and a negative part is a different kind of comparison altogether.