A ratio such as 3 : 5 packs two different fractions into one expression. Read one way, it compares the parts with each other: the first group is 3/5 the size of the second. Read another way, it describes how a whole is divided: the first group makes up 3/8 of everything. Confusing the two is one of the most common ratio mistakes in school math and in news reports. This calculator gives both, with decimals, percentages and a tape diagram — the bar model used in many US classrooms.
How to use the ratio to fraction calculator
- Type a ratio with colons, such as
3:5or2:3:4. Decimals and fractions are allowed. - Optionally name the parts, separated by commas (
boys, girlsorred, blue, green), so the results read naturally. - The tape lists each part’s fraction of the whole with its decimal and percent, then the part-to-part fractions.
- The diagram splits a bar into equal units, colored by part, so you can see the whole at a glance.
Ratio to fraction formulas
For a ratio a : b:
With more terms, the whole is the sum of every term: in a : b : c, the first part is a/(a + b + c).
Worked example: a class of students
A class has boys and girls in the ratio 3 : 5.
Count the parts: 3 + 5 = 8 equal parts make the whole class
Boys as a fraction of the class: 3/8 = 0.375 = 37.5%
Girls as a fraction of the class: 5/8 = 0.625 = 62.5%
Boys compared with girls: 3/5 — there are three-fifths as many boys as girls
If the class has 32 students: one part is 32 ÷ 8 = 4, so there are 12 boys and 20 girls
Reading a tape diagram
The bar model draws every unit of the ratio as an equal box. For 3 : 5 you see three boxes of one color and five of another, eight in total. The picture makes the part-to-whole fractions obvious — three of the eight boxes — and it scales to real numbers: if the whole bar stands for 32 students, each box stands for 4. When a ratio is not in simplest form, the diagram uses the simplified version so the boxes stay countable.
Part-to-part vs. part-to-whole in the real world
| Statement | Ratio | Fraction it implies |
|---|---|---|
| “Mix concentrate and water 1 : 4” | Part-to-part | Concentrate is 1/5 of the drink |
| “The odds are 1 to 3” | Part-to-part | The chance is 1/4, or 25% |
| “3 of every 10 voters chose Smith” | Part-to-whole | 3/10, or 30% |
| “Students to teachers is 18 : 1” | Part-to-part | Teachers are 1/19 of the people in the room |
Odds are a classic trap: odds of 1 to 3 mean one success for every three failures, so the probability is 1 out of 4, not 1 out of 3.
Tips
- Simplify last. The fraction 6/16 from a 6 : 10 ratio reduces to 3/8 — the same answer as starting from 3 : 5. Use the ratio simplifier if you’d like the ratio itself in lowest terms.
- Percentages must add to 100%. If your part-to-whole percents don’t total 100%, one of the terms was left out of the sum.
- Keep units consistent. “250 mL to 1 L” must become 250 : 1,000 = 1 : 4 before you convert.
For proportions with a missing term or for splitting an amount by a ratio, the ratio calculator has dedicated modes. To turn a fraction into a percent with repeating decimals handled exactly, use the fraction to percent calculator.
Frequently asked questions
How do you convert a ratio to a fraction?
For a part-to-whole fraction, put one term over the sum of all the terms. In a class with a boys-to-girls ratio of 3:5, there are 8 parts in all, so 3/8 of the class are boys and 5/8 are girls.
What is the difference between part-to-part and part-to-whole?
Part-to-part compares one group with another group (boys to girls, 3/5). Part-to-whole compares one group with the total (boys to all students, 3/8). Both come from the same ratio but answer different questions.
Is the ratio 3:5 the same as the fraction 3/5?
It is the same as the part-to-part fraction 3/5, meaning the first quantity is 3/5 the size of the second. It is not the fraction of the whole: the first quantity is 3/8 of the total.
How do I convert a three-part ratio to fractions?
Add all three terms for the whole and divide each term by that sum. For 2:3:4 the whole is 9, giving 2/9, 3/9 = 1/3 and 4/9.
How do I turn a ratio into a percentage?
Convert the part-to-whole fraction to a percent. In the ratio 3:5 the first part is 3/8 = 0.375 = 37.5% of the total.