Ratio Calculator
Reduce a ratio to its simplest form, solve a proportion for a missing value, or scale a ratio up or down to a new size.
Result
- As a fraction (A ÷ B)
- 0.75
- A as a share of the total
- 42.86%
- B as a share of the total
- 57.14%
- Equivalent ratios
- 6 : 8, 9 : 12, 30 : 40
What is a ratio?
A ratio expresses how much of one thing there is compared with another. A recipe that calls for 2 cups of flour to 3 cups of water has a flour-to-water ratio of 2 : 3. Ratios are used for mixing paint and concrete, scaling recipes, map scales, screen resolutions (16 : 9) and financial measures such as the debt-to-income ratio. The order matters: 2 : 3 is not the same as 3 : 2.
Formulas
Simplifying: divide both terms by their greatest common divisor (GCD). 6 : 8 → GCD is 2 → 3 : 4.
Proportion: if A : B = C : D then A × D = B × C. For 2 : 3 = C : 9, C = (2 × 9) ÷ 3 = 6.
Scaling: multiply both terms by the same factor. 3 : 4 scaled by 2.5 is 7.5 : 10; the ratio is unchanged because both parts grew together.
Worked example: a photo is 6 inches by 8 inches. Simplifying 6 : 8 gives 3 : 4, so the picture has the classic 4 : 3 landscape proportions turned on its side. To enlarge it so the short side becomes 9 inches, solve 6 : 8 = 9 : D, giving D = 8 × 9 ÷ 6 = 12 inches.
How to use this calculator
- Simplify: enter A and B. Decimals are converted to whole numbers before reducing.
- Solve a proportion: fill in three of A, B, C and D and leave the unknown blank; the calculator finds it by cross-multiplying.
- Scale: enter the ratio and a multiplier such as 2 (double) or 0.5 (halve).
Tips
- To compare more than two quantities, simplify them pairwise or divide all of them by their common GCD.
- A ratio of a part to the whole is a fraction; convert it to a percentage with the percentage calculator.
- Ratios with the same simplified form are equivalent: 3 : 4, 6 : 8 and 75 : 100 all describe the same relationship.
- For arithmetic on fractions themselves, see the fraction calculator.
Frequently asked questions
What is a ratio?
A ratio compares two quantities by division. "3 : 4" (read "three to four") means that for every 3 of the first thing there are 4 of the second. Ratios can be written with a colon, as a fraction (3/4) or with the word "to".
How do I simplify a ratio with decimals?
Multiply both parts by a power of ten until they are whole numbers, then divide both by their greatest common divisor. 1.5 : 2 becomes 15 : 20, and dividing by 5 gives 3 : 4. The calculator does this automatically.
How do I solve a proportion?
Cross-multiply. If a : b = c : d then a × d = b × c. Solve that equation for the unknown. For 2 : 3 = x : 9, cross-multiplying gives 3x = 18, so x = 6.
What is the difference between a ratio and a fraction?
A fraction is a part compared with the whole, whereas a ratio usually compares one part with another part. If a class has 3 boys for every 4 girls the ratio of boys to girls is 3 : 4, but boys are 3/7 of the class.