Ratio Calculator
Separate the parts with colons, like 12 : 18 or 3 : 4 : 5 (up to 4 parts).
A ratio compares amounts by how many parts of each there are. Use this ratio calculator to simplify a ratio, find the missing number in a proportion such as 3 : 4 = 15 : x, or share an amount in a given ratio. Every answer comes with the steps and a bar showing the parts.
Multiplying or dividing every part by the same number keeps the ratio the same
Three Kinds of Ratio Problem
Almost every ratio question is one of these. Each one is a tab in the calculator above.
Simplify
Divide every part by the greatest common factor, just like simplifying a fraction.
Solve a Proportion
Two equal ratios with one number missing. Find the scale factor, or cross-multiply.
Split an Amount
Add the parts, find what one part is worth, then multiply.
A Ratio Isn't a Fraction of the Whole
Sharing $100 in the ratio 2 : 3 gives the first person 2 of the 5 parts, not 2 of 3.
The shares should add back up to the amount you started with ($40 + $60 = $100), and their ratio should simplify to the one you were given (40 : 60 = 2 : 3).
Ratios You Already Use
Recipes, maps and screens all work by keeping a ratio the same while the sizes change.
| Where | Ratio | Example |
|---|---|---|
| Recipe | 4 servings : 300 g | 6 servings need 300 ÷ 4 × 6 = 450 g |
| Map scale | 1 : 50,000 | 4.5 cm on the map is 225,000 cm = 2.25 km |
| Screen | 16 : 9 | 1,920 pixels wide → 1,920 ÷ 16 × 9 = 1,080 tall |
| Concrete mix | 1 : 2 : 3 | cement : sand : gravel, 6 parts in total |
| Drink mix | 1 : 4 | 250 ml of squash makes 1.25 L in all |
Ratios on a 4 Function Calculator
Each ratio problem is a multiplication and a division on a basic calculator.
3 : 4 = 15 : x
$100 in 2 : 3
Unit Ratio of 12 : 18
Practise all three kinds of problem in Ratios and Proportions: How to Simplify, Solve and Share.
Explore Other Calculators
Frequently Asked Questions
How do you simplify a ratio?
Divide every part by their greatest common factor. 12 : 18 has a GCF of 6, so it simplifies to 2 : 3. With decimals, multiply every part by 10 or 100 first: 0.5 : 2 becomes 5 : 20, which is 1 : 4.
How do you solve a proportion?
Write both ratios as fractions and cross-multiply. For 3 : 4 = 15 : x, 3 × x = 4 × 15 = 60, so x = 60 ÷ 3 = 20. Or use the scale factor: 3 × 5 = 15, so x = 4 × 5 = 20.
How do you split an amount in a ratio?
Add the parts, find one part, then multiply. $100 in the ratio 2 : 3 is 5 parts, so one part is 100 ÷ 5 = 20 and the shares are $40 and $60.
Is a ratio the same as a fraction?
Not quite. 2 : 3 compares two parts with each other; a fraction compares a part with the whole. In a 2 : 3 split, the first share is 2/5 of the total, not 2/3, because there are 5 parts altogether.
What is a unit ratio?
A ratio written with 1 as one of its parts, such as 1 : 1.5 or 1 : 50,000. Divide every part by the first part to get it. Map scales use unit ratios because they make comparisons easy.
Does the order of a ratio matter?
Yes. With 2 boys for every 3 girls, boys to girls is 2 : 3 but girls to boys is 3 : 2. Keep the parts in the order the question names them.