What a ratio is
A ratio compares amounts. A ratio a:b, read "a to b", says that for every a of the first thing there are b of the second. A pancake recipe with flour and milk in the ratio 2:3 uses 2 cups of flour for every 3 cups of milk, and 4 cups of flour for 6 cups of milk. Both describe the same mix, so 2:3 and 4:6 are equivalent ratios. Ratios can have more than two parts, like 1:2:3 for three ingredients.
Solving a proportion with cross multiplication
A proportion says that two ratios are equal. When one of the four values is missing, you can solve for x by cross multiplying: multiply the outer terms and the inner terms, set the products equal and divide.
Example: a recipe for 4 people uses 3 eggs. How many eggs for 20 people? Write 3:4 = x:20. Cross multiply: 3 × 20 = 4 × x, so 60 = 4x and x = 15 eggs.
Simplifying ratios
To simplify a ratio, divide every part by the greatest common divisor (GCD), the largest whole number that divides all of them. 12:18 has a GCD of 6, so it simplifies to 2:3. If the ratio has decimals, multiply all parts by 10, 100 or 1000 first to make them whole numbers. For 1.5:2.25 multiply by 100 to get 150:225, then divide by the GCD of 75 to get 2:3. Fractions work the same way, using the common denominator: 1/2:1/3 times 6 is 3:2.
Scaling a ratio and splitting a total
To split an amount in a ratio, add the parts, divide the amount by that sum, and multiply each part. Sharing $300 in the ratio 2:3:5 gives 10 parts of $30 each, so the shares are $60, $90 and $150. To scale a ratio to a known value, find the scale factor and multiply every part by it. If a 2:3:5 mix needs 8 liters of the first part, the factor is 8 ÷ 2 = 4, and the full mix is 8:12:20.
Maps use ratios too. A scale of 1:50,000 means 1 cm on the map is 50,000 cm, or 500 meters, on the ground. So 4 cm on the map is 2 km.
Aspect ratios
The aspect ratio of a screen, photo or video is its width to its height. 1920 × 1080 simplifies to 16:9, because both divide by 120. To keep the shape when resizing, solve a proportion: a 16:9 video that is 1280 pixels wide is 1280 × 9 ÷ 16 = 720 pixels high.
| Aspect ratio | Common use | Example sizes in pixels |
|---|---|---|
| 16:9 | TV, YouTube, most monitors | 1920 × 1080, 3840 × 2160 |
| 4:3 | Older screens, iPad | 1024 × 768, 1600 × 1200 |
| 3:2 | Camera photos | 6000 × 4000 |
| 1:1 | Square social posts | 1080 × 1080 |
| 4:5 | Portrait social posts | 1080 × 1350 |
| 9:16 | Phone video, stories, reels | 1080 × 1920 |
How to use the ratio calculator
- 1Pick what you want to do: solve a proportion, simplify a ratio, scale it, or compare two ratios.
- 2Type the numbers. Use a colon between parts, like 16:9. To solve a proportion, leave the missing box empty or type x.
- 3Read the answer and the steps below it, including the cross multiplication. Copy the result or a link that keeps your numbers.
Frequently asked questions
How do I solve a proportion?
Cross multiply. In 3:4 = x:20, write it as 3/4 = x/20, then multiply across: 3 × 20 = 4 × x, so 60 = 4x. Divide both sides by 4 and you get x = 15. The calculator works the same way whichever of the four values is missing.
How do I simplify a ratio with decimals?
First multiply every term by 10, 100 or 1000 so that all of them become whole numbers. Then divide by their greatest common divisor. For 1.5:2.25, multiply by 100 to get 150:225. The GCD of 150 and 225 is 75, so the ratio simplifies to 2:3.
How do I split an amount in a ratio?
Add the parts of the ratio, divide the amount by that sum, and multiply each part by the result. To split 300 in the ratio 2:3:5, the parts add up to 10, one part is 300 ÷ 10 = 30, and the shares are 60, 90 and 150.
How can I tell if two ratios are equivalent?
For two-part ratios, cross multiply. 2:3 and 6:9 are equivalent because 2 × 9 = 18 and 3 × 6 = 18. You can also simplify both: if they reduce to the same ratio, here 2:3, they are equivalent. That second test also works for ratios with three or more parts.
Is a ratio the same as a fraction?
Closely related, but not the same. The ratio 2:3 compares two amounts with each other, while the fraction 2/3 compares a part to a whole. In a 2:3 mix, the first part is 2/5 of the total, not 2/3, because the whole has 2 + 3 = 5 parts.