Ratio and Proportion Calculator
Simplify a ratio, split an amount in a given ratio, or find the missing number in a proportion. You can type decimals and fractions, and each result comes with the working so you can follow the steps.
Your result
Enter your numbers above to see the result.
Results are exact for the values you type. Decimal figures are rounded for display only.
Ratios in everyday life
A ratio is a way of comparing amounts. You meet them in recipes, paint mixes, map scales, screen sizes, school grades and the way a bill gets split between friends. When someone says “mix one part concentrate to four parts water”, or “the map is 1 to 50,000”, they are giving you a ratio, and the useful question is always what that means for the amounts you actually have.
This calculator covers the three things people most often need to do. It simplifies a ratio into its smallest whole numbers, divides a total into shares that follow a ratio, and finds the missing number in a proportion. It accepts decimals and fractions, keeps the arithmetic exact, and shows the working.
How to use this calculator
- Simplify: type the parts of your ratio, one per box. You get the simplest whole-number ratio, each part as a fraction and percentage of the whole, and the ratio written in the form 1 : n.
- Divide an amount: enter the ratio parts, then the total to share. You get each share and its percentage of the total.
- Solve a proportion: fill in three of the four boxes and leave one empty. The calculator finds the missing value and shows the cross-multiplication. Fill all four boxes to check whether two ratios are really equal.
The rules behind it
Simplify: divide every part by the greatest common divisor
Share of a part = total × part ÷ sum of all parts
Direct proportion: A ÷ B = C ÷ D, so A × D = B × C
Inverse proportion: A × B = C × D
With decimals or fractions, every part is first converted to a whole number by multiplying them all by the same factor. For example, 0.75 : 1/2 is the same as 3/4 : 2/4, and multiplying both by 4 gives 3 : 2. Because the calculator works with exact fractions rather than rounded decimals, you do not get small errors from floating-point arithmetic.
Worked examples
Simplifying
12 : 18 : 24. The largest number that divides all three is 6, so the ratio simplifies to 2 : 3 : 4. For 1.5 : 2.5, multiply both by 2 to get 3 : 5.
Dividing an amount
Share 400 in the ratio 3 : 2. There are 5 parts, so one part is 400 ÷ 5 = 80. The shares are 3 × 80 = 240 and 2 × 80 = 160. For a three-way split of 1,000 in the ratio 5 : 3 : 2, one part is 100 and the shares are 500, 300 and 200.
Scaling a recipe
A recipe uses 250 g of flour for 4 people and you are cooking for 6. Set up 250 : 4 = x : 6. Cross-multiplying gives 4x = 1,500, so x = 375 g.
Reading a map
On a 1 : 50,000 map, a route measures 3.2 cm. In real life that is 3.2 × 50,000 = 160,000 cm, which is 1.6 km.
An inverse proportion
Six workers need 10 days to finish a job. How long would 15 workers take? More workers means fewer days, so the product stays the same: 6 × 10 = 15 × d, and d = 4 days.
Common ratios as percentages
A two-part ratio is easy to turn into a split of 100. Divide each part by the total of both parts.
| Ratio | First part | Second part |
|---|---|---|
| 1 : 1 | 50% | 50% |
| 1 : 2 | 33.33% | 66.67% |
| 1 : 3 | 25% | 75% |
| 1 : 4 | 20% | 80% |
| 2 : 3 | 40% | 60% |
| 3 : 2 | 60% | 40% |
| 3 : 7 | 30% | 70% |
| 1 : 9 | 10% | 90% |
Common mistakes
- Treating a part-to-part ratio as part-to-whole. In 3 : 2, the first share is 3/5 of the total, not 3/2.
- Mixing units. Convert both quantities to the same unit first, so 2 m : 50 cm is 200 : 50, which is 4 : 1.
- Putting the numbers in the wrong order. 3 : 2 and 2 : 3 are different ratios.
- Using direct proportion where the relationship is inverse, such as workers and days or speed and travel time.
- Rounding too early. Keep the exact values and round only the final answer.
Aspect ratios
The ratio of a screen or image’s width to its height is called the aspect ratio. Enter the width and height on the Simplify tab to find it. 1920 × 1080 gives 16 : 9, and 1024 × 768 gives 4 : 3. If you want to resize an image and keep its shape, set up a proportion with the old width and height and the new width and solve for the new height.
Frequently asked questions
What is a ratio?
A ratio compares two or more quantities of the same kind. If a drink is mixed from 1 part concentrate and 4 parts water, the ratio of concentrate to water is 1 : 4. It says nothing about the actual amounts, only how they compare, so 1 : 4 describes 50 ml with 200 ml just as well as 1 litre with 4 litres.
How do I simplify a ratio?
Divide every part by the largest number that divides them all, which is the greatest common divisor. For 12 : 18 : 24, that number is 6, so the simplified ratio is 2 : 3 : 4. If the parts are decimals or fractions, first multiply them all by the same number to turn them into whole numbers. The calculator does this for you.
How do I divide an amount in a given ratio?
Add up the parts, divide the total by that sum to find the size of one part, then multiply by each part. To share 400 in the ratio 3 : 2, there are 5 parts, one part is 80, and the shares are 240 and 160. Use the Divide an amount tab for any number of parts.
What is the difference between a ratio and a fraction?
A fraction compares a part with the whole, while a ratio can compare a part with another part. In a 3 : 2 ratio, the first share is 3/5 of the total, not 3/2. The Simplify tab shows both the ratio and the fraction and percentage of the whole for each part.
How do I solve a proportion?
A proportion says two ratios are equal, such as 2 : 3 = 4 : x. Cross-multiply to get 2 × x = 3 × 4, so x = 12 ÷ 2 = 6. In the Solve a proportion tab, fill in three of the four boxes, leave the fourth empty, and the calculator finds it and shows the cross-multiplication.
What is inverse proportion?
In a direct proportion, when one quantity doubles, the other doubles too. In an inverse proportion, when one doubles, the other halves. If 6 workers take 10 days to finish a job, 15 workers take 4 days, because the product 6 × 10 = 15 × 4 stays the same. Choose Inverse in the Solve a proportion tab for cases like this.
Can I enter decimals and fractions?
Yes. You can type decimals such as 2.5 and fractions such as 3/4 in any box. They are handled as exact values, so 0.75 : 1/2 simplifies exactly to 3 : 2 with no rounding error.
How do I turn a ratio into a percentage?
Divide each part by the total of all the parts and multiply by 100. For 3 : 7 the total is 10, so the parts are 30% and 70%. The Simplify tab shows this table automatically.
How do I find a screen's aspect ratio?
Enter the width and height and simplify. 1920 × 1080 simplifies to 16 : 9, and 1024 × 768 simplifies to 4 : 3. Some sizes, such as 1366 × 768, do not simplify to small numbers because the pixel counts were rounded from a common ratio.
Is anything I enter saved or sent anywhere?
No. The sums run in your browser and nothing you type is uploaded or stored on our servers.
Related calculators
To work with parts of a whole, use the fraction calculator or the percentage calculator. To describe a set of numbers, try the average calculator, and for splitting a bill, the tip and bill split calculator.