Ratio Calculator
Enter three values and leave the unknown blank. It finds the missing one.
A ratio compares two or more amounts, like 2 parts flour to 1 part water, written 2:1. This calculator handles the four things people actually need: solving a missing value in A:B = C:D, simplifying a messy ratio down to whole numbers, checking whether two ratios are equal, and scaling a ratio up to a target total. Pick a mode above, type your numbers, and you get the answer plus every step. Below you will find worked examples, quick-reference tables, and clear answers for the exact problems people search, from "how to solve ratios" to "select all ratios equivalent to 2:1".
What is a ratio?
A ratio shows how two quantities relate in size. If a recipe uses 3 cups of rice for every 2 cups of beans, the ratio of rice to beans is 3:2. You read it "three to two". Ratios can compare part to part (rice to beans, 3:2) or part to whole (rice to total, 3:5, since 3 + 2 = 5 total parts). The order matters. 3:2 is not the same as 2:3, because the first number always refers to the first quantity named.
Ratios do not carry units in the final form. A ratio of 3:2 works whether you measure in cups, liters, or truckloads, as long as both sides use the same unit before you compare them.
How do you calculate a ratio?
To find the ratio between two numbers, write them in order separated by a colon, then divide both by their greatest common divisor to simplify. Say you have 12 boys and 18 girls in a class. The ratio of boys to girls is 12:18. The greatest common divisor of 12 and 18 is 6, so divide both sides: 12 ÷ 6 = 2 and 18 ÷ 6 = 3. The simplified ratio is 2:3.
That is the whole method in three steps: write the numbers in the right order, find the largest number that divides into both, and divide each side by it. Use the Simplify tab above to do this instantly for two or three numbers, decimals included.
How do you solve ratios (find a missing value)?
When two ratios are equal, they form a proportion, written A:B = C:D. To find a missing term you cross-multiply: A × D = B × C. Solve that equation for the unknown.
Example. You know 3:4 = 9:? and want the missing fourth value. Cross-multiply the known diagonal against the unknown. Here 3 × D = 4 × 9, so 3D = 36, which gives D = 12. The complete proportion is 3:4 = 9:12. Enter 3, 4, 9 in the "A:B = C:D" tab and leave the last box blank, and the tool returns 12 with the working shown.
Another. Solve 2:5 = ?:20. The unknown is in the C position. Cross-multiply: 2 × 20 = 5 × C, so 40 = 5C, and C = 8. The proportion is 2:5 = 8:20.
Common ratio problems solved
Here are worked answers to problems people paste in most often. Each one is solved by cross-multiplication or simplifying.
| Problem | Method | Answer |
|---|---|---|
| 3:4 = 9:? | 4 × 9 ÷ 3 | 12 |
| 2:5 = ?:20 | 2 × 20 ÷ 5 | 8 |
| 1:2 = ?:16 | 1 × 16 ÷ 2 | 8 |
| 5:8 = 15:? | 8 × 15 ÷ 5 | 24 |
| 7:3 = ?:9 | 7 × 9 ÷ 3 | 21 |
| 4:6 = 10:? | 6 × 10 ÷ 4 | 15 |
How do you check if two ratios are equivalent?
Two ratios are equivalent when they simplify to the same lowest form, or when their cross products match. The fastest check is cross-multiplication: for A:B and C:D, if A × D equals B × C, the ratios are equal.
Take a common textbook question: are the ratios 6:2 and 9:3 equivalent? Cross-multiply: 6 × 3 = 18 and 2 × 9 = 18. The products match, so yes, 6:2 and 9:3 are equivalent. Both also reduce to 3:1, which confirms it.
Try another: are 4:2 and 10:5 equivalent? 4 × 5 = 20 and 2 × 10 = 20. Equal products, so yes. Both simplify to 2:1. To test any pair yourself, simplify each one in the Simplify tab. If both return the same result, they are equivalent. For a full missing-value proportion, our proportion calculator shows the cross-multiplication step by step.
Select all ratios equivalent to 2:1, 1:2, 3:2 and more
A ratio is equivalent to another when both simplify to the same lowest form. The quick test is to divide the first number by the second and compare. This table lists the equivalents students are asked to identify most often.
| Base ratio | Equivalent ratios | Quick test |
|---|---|---|
| 2:1 | 4:2, 6:3, 8:4, 10:5, 20:10 | first ÷ second = 2 |
| 1:2 | 2:4, 3:6, 4:8, 5:10, 50:100 | second ÷ first = 2 |
| 3:2 | 6:4, 9:6, 12:8, 15:10, 30:20 | first ÷ second = 1.5 |
| 5:4 | 10:8, 15:12, 20:16, 25:20 | first ÷ second = 1.25 |
| 1:1 | 2:2, 3:3, 5:5, 10:10, 50:50 | both sides equal |
| 4:1 | 8:2, 12:3, 16:4, 20:5, 40:10 | first ÷ second = 4 |
For a multiple-choice question like "select all ratios equivalent to 2:1", simplify each option in the Simplify tab. Every option that returns 2:1 belongs on the list. For 8:4, dividing both by 4 gives 2:1, so it qualifies. For 6:4, it reduces to 3:2, so it does not.
How do you simplify a ratio?
Simplifying a ratio means dividing every term by their greatest common divisor until no whole number bigger than 1 divides them all. Simplify 8:12:20. The greatest common divisor of 8, 12, and 20 is 4. Divide each: 8 ÷ 4 = 2, 12 ÷ 4 = 3, 20 ÷ 4 = 5. The simplest form is 2:3:5.
Decimals work too. To simplify 2.5:5, first clear the decimal by multiplying both sides by 10, giving 25:50, then divide by the common divisor 25 to get 1:2. The Simplify tab does both steps automatically and shows them.
How do you scale a ratio to a total?
Scaling splits a target amount according to the ratio. Suppose you mix a 2:3 solution and need 50 ml total. Add the parts: 2 + 3 = 5 parts. Each part is 50 ÷ 5 = 10 ml. So the 2-part side gets 2 × 10 = 20 ml and the 3-part side gets 3 × 10 = 30 ml. The split is 20:30, which still simplifies back to 2:3.
This is how you divide money, ingredients, or paint by a ratio. Use the "Scale A:B" tab, enter the ratio, choose "Target total", and type the total. It returns each share.
What do common ratios mean?
People search specific ratios wanting a plain-English meaning. This table gives the reading and a real-world use for each.
| Ratio | Meaning | Where you see it |
|---|---|---|
| 1:1 | Equal amounts of both | 50/50 mixes, even splits |
| 2:1 | Twice as much of the first | Concrete mix, dilutions |
| 3:1 | Three parts to one part | Cocktails, cleaning solutions |
| 3:2 | Three parts to two parts | Recipes, some screen sizes |
| 4:1 | Four parts to one part | Fuel mixes, paint thinning |
| 1:2 | Half as much of the first | Rice to water, syrups |
| 1:5 | One part to five parts | Strong dilutions |
How do you convert a ratio to a fraction, percentage, or decimal?
A ratio A:B can be written as the fraction A/B, then turned into a decimal by dividing, and into a percentage by multiplying the decimal by 100. Part-to-whole ratios convert most cleanly to percentages. This table shows the common conversions people look up.
| Ratio | Fraction | Decimal | Percentage |
|---|---|---|---|
| 1:2 | 1/2 | 0.5 | 50% |
| 1:3 | 1/3 | 0.333 | 33.3% |
| 1:4 | 1/4 | 0.25 | 25% |
| 2:3 | 2/3 | 0.667 | 66.7% |
| 3:4 | 3/4 | 0.75 | 75% |
| 1:5 | 1/5 | 0.2 | 20% |
| 3:2 | 3/2 | 1.5 | 150% |
To go the other way, a percentage becomes a ratio over 100. So 25% is 25:100, which simplifies to 1:4. Our percentage calculator helps when you need to move between percentages and parts.
Part to part vs part to whole ratios
A part-to-part ratio compares one group to another. In a bag of 3 red and 5 blue marbles, red to blue is 3:5. A part-to-whole ratio compares one group to the total. Red to all marbles is 3:8, because there are 8 marbles in total. The difference matters in word problems: "the ratio of red to blue" needs part to part, while "what fraction are red" needs part to whole. Same numbers, different denominator.
Ratios and order of operations
When a ratio problem sits inside a larger calculation, solve what is in brackets and handle multiplication and division before you compare terms. If you are ever unsure which step comes first in a multi-part expression, the BODMAS calculator walks through the correct order so your ratio inputs are right before you simplify.