Ratio Calculator
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C = 15, so 3 : 4 = 15 : 20
3 : 4 = C : 20 1. In a true proportion the cross products are equal: A × D = B × C. 2. 3 × 20 = 4 × C 3. C = 3 × 20 ÷ 4 = 60 ÷ 4 = 15 Check: 3 : 4 and 15 : 20 both simplify to 3 : 4.
How to use the ratio calculator
- Choose what you want to do: solve A : B = C : D, simplify a ratio, or split a total.
- To solve a proportion, fill in three of A, B, C and D and leave the unknown blank.
- To simplify or split, type the ratio with colons, such as
12 : 18 : 30. Up to 10 terms are allowed, and terms can be decimals (1.5) or fractions (3/4). - Read the answer and open the step-by-step working. When a value does not end, such as 100 ÷ 3, the exact fraction is shown next to the rounded decimal.
Ratio formulas
Simplify: divide every term by GCF(A, B, …)
Split a total T in A : B : C: share of A = T × A ÷ (A + B + C)
A as a fraction of the whole = A ÷ (A + B + …)
A ratio compares quantities by how many times one contains the other: 2 : 3 means that for every 2 of the first there are 3 of the second. Multiplying or dividing every term by the same number gives an equivalent ratio, which is why simplifying uses the greatest common factor (GCF) and why a proportion, two equal ratios, can be solved by cross-multiplying. Here A, B, C and D are the terms and T is the amount being shared.
Worked examples
Solving 3 : 4 = x : 20
Cross-multiply: 3 × 20 = 4 × x, so x = 60 ÷ 4 = 15. Both 3 : 4 and 15 : 20 simplify to the same ratio, and the second is the first scaled by 5.
Simplifying 12 : 18 : 30 and 1.5 : 2.5
The GCF of 12, 18 and 30 is 6, so 12 : 18 : 30 = 2 : 3 : 5. For 1.5 : 2.5, multiply both terms by 2 to clear the decimals (3 : 5); their GCF is 1, so the simplest form is 3 : 5.
Sharing 120 in the ratio 1 : 2 : 3
There are 1 + 2 + 3 = 6 parts, each worth 120 ÷ 6 = 20, so the shares are 20, 40, 60. They add back up to 120, which is a quick check.
Scaling a recipe
A dressing uses oil and vinegar in the ratio 2 : 3. With 5 tablespoons of oil, the vinegar needed is 3 × 5 ÷ 2 = 7.5 tablespoons, from 2 : 3 = 5 : x.
Common ratios as fractions and percentages
| Ratio | Simplest form | Fractions of the whole | Percentages |
|---|---|---|---|
| 1 : 1 | 1 : 1 | 1/2, 1/2 | 50%, 50% |
| 1 : 2 | 1 : 2 | 1/3, 2/3 | ≈ 33.33%, ≈ 66.67% |
| 1 : 3 | 1 : 3 | 1/4, 3/4 | 25%, 75% |
| 2 : 3 | 2 : 3 | 2/5, 3/5 | 40%, 60% |
| 1 : 4 | 1 : 4 | 1/5, 4/5 | 20%, 80% |
| 3 : 5 | 3 : 5 | 3/8, 5/8 | 37.5%, 62.5% |
| 3 : 7 | 3 : 7 | 3/10, 7/10 | 30%, 70% |
| 1 : 9 | 1 : 9 | 1/10, 9/10 | 10%, 90% |
| 4 : 6 | 2 : 3 | 2/5, 3/5 | 40%, 60% |
| 2 : 3 : 5 | 2 : 3 : 5 | 1/5, 3/10, 1/2 | 20%, 30%, 50% |
| 1 : 1 : 2 | 1 : 1 : 2 | 1/4, 1/4, 1/2 | 25%, 25%, 50% |
Tips and common mistakes
- Order matters. 2 : 3 and 3 : 2 are different ratios. Keep the terms in the order the problem gives them.
- A ratio is not a fraction of the whole. In 3 : 5 the first part is 3/8 of the total, not 3/5. Use the percentages table or the calculator's simplify mode to see the parts.
- Use the same units. Before comparing 30 cm to 2 m, convert to 30 : 200, which simplifies to 3 : 20.
- Rounded shares may not add up. 100 split 1 : 2 gives 33.33 and 66.67 when rounded to cents, which still totals 100.00 here, but with more parts the rounding can leave a cent over; adjust one share.
- To work with fractions directly, use the fraction calculator; for percentages of a number, the percentage calculator.
Frequently asked questions
How do I simplify a ratio?
Divide every term by their greatest common factor. For 12 : 18 the GCF is 6, so 12 : 18 = 2 : 3. With three terms it works the same way: 12 : 18 : 30 = 2 : 3 : 5.
How do I solve a proportion such as 3 : 4 = x : 20?
Cross-multiply: in A : B = C : D the products A × D and B × C are equal. So 3 × 20 = 4 × x, which gives x = 60 ÷ 4 = 15. Check: 15 : 20 simplifies back to 3 : 4.
How do I split an amount in a given ratio?
Add the terms to get the number of parts, divide the total by that, then multiply by each term. To split 120 in the ratio 1 : 2 : 3, there are 6 parts of 120 ÷ 6 = 20, so the shares are 20, 40 and 60.
How do I turn a ratio into percentages?
Divide each term by the sum of the terms and multiply by 100. For 3 : 5 there are 8 parts, so the first share is 3/8 = 37.5% and the second is 5/8 = 62.5%. A ratio of 3 : 5 does not mean 3/5 of the whole.
Can a ratio have decimals or fractions?
Yes, but it is usually written with whole numbers. Multiply every term by the same number to clear the decimals, then simplify: 1.5 : 2.5 becomes 3 : 5 after multiplying by 2, and 1/2 : 1/3 becomes 3 : 2 after multiplying by 6.