What is a ratio?
A ratio is a simple way of comparing two or more quantities. If a recipe uses 2 cups of rice for every 3 cups of water, the ratio of rice to water is 2 to 3, written 2:3. The actual cups don't matter. What matters is the relationship, which stays the same whether you cook for two people or twenty.
You meet ratios far more often than you might think: mixing paint, scaling a recipe, reading a map, comparing prices, choosing a screen size (16:9 is a ratio) or deciding how to split a bill. The maths is always the same handful of moves, and this page does them for you and shows its working.
Three ways to write a ratio
- With a colon: 3:2
- With the word "to": 3 to 2
- As a fraction: 3/2 (handy when you compare just two quantities)
How to use the ratio calculators
Choose the tab that matches your problem, type your numbers and press the button. You get the answer first, then two explanations: a numbered walk-through in words, and the same working written the way you would on paper, with fractions and equals signs.
Ratio formulas you can rely on
When two ratios are equal we call it a proportion, written A : B = C : D. The key fact is that A × D always equals B × C (this is called cross-multiplying). Rearranging that gives a formula for whichever number is missing:
- A = (B × C) ÷ D
- B = (A × D) ÷ C
- C = (A × D) ÷ B
- D = (B × C) ÷ A
To simplify a ratio, divide every number by their greatest common divisor (GCD). To split a total, divide it by the sum of the parts and multiply by each part. To get percentages, divide each part by the sum of all the parts and multiply by 100. To scale a ratio, multiply every part by the same factor.
Worked examples
Finding a missing value
Write 3 : 2 = C : 14. Then C = (3 × 14) ÷ 2 = 21.
Simplifying a ratio
The GCD of 40, 60 and 100 is 20, so divide each by 20 to get 2 : 3 : 5.
Splitting an amount
Three friends invest in the ratio 5 : 3 : 2 and want to share a profit of 500 the same way. The parts add up to 10, so one part is 500 ÷ 10 = 50.
| Person | Ratio part | Calculation | Share |
|---|---|---|---|
| Friend 1 | 5 | 5 × 50 | 250 |
| Friend 2 | 3 | 3 × 50 | 150 |
| Friend 3 | 2 | 2 × 50 | 100 |
Ratio to percentage
More ratio tools
These four calculators build on the same ideas. Tap one to jump straight to it.
Scaling a ratio
Comparing two ratios
Aspect ratio and resizing
A 1920 × 1080 screen simplifies to 16 : 9. To shrink it to 1280 wide without stretching, set up 16 : 9 = 1280 : H. Then H = (9 × 1280) ÷ 16 = 720. Common aspect ratios:
| Ratio | Typical use | Example size |
|---|---|---|
| 16 : 9 | Widescreen video, most monitors, YouTube | 1920 × 1080 |
| 4 : 3 | Classic TVs and older monitors | 1024 × 768 |
| 1 : 1 | Square social posts | 1080 × 1080 |
| 9 : 16 | Vertical video such as Stories and Reels | 1080 × 1920 |
| 3 : 2 | 35 mm film and many cameras | 3000 × 2000 |
| 21 : 9 | Ultrawide monitors and cinema | 2560 × 1080 |
The golden ratio
The golden ratio, written φ (phi), is (1 + √5) ÷ 2, which is about 1.618. If you cut a 100 cm board in the golden ratio, the longer piece is 100 ÷ 1.618 ≈ 61.8 cm and the shorter piece is 38.2 cm. Designers use it for layouts, logos and picture frames because the proportion feels balanced to many people.
Ratio, fraction or percent?
These three describe the same idea from different angles, and it helps to hop between them. Take a class of 12 boys and 18 girls:
| Form | Boys and girls | What it tells you |
|---|---|---|
| Ratio | 12:18, simplified 2:3 | For every 2 boys there are 3 girls |
| Fraction of the whole | 12/30 = 2/5 are boys | Two fifths of the class |
| Percentage | 40% boys, 60% girls | The same fractions scaled to 100 |
A common slip is mixing up part-to-part and part-to-whole. A 2:3 ratio has 5 parts in total, so the boys are two fifths of the class, not two thirds.
Everyday places ratios show up
Common mistakes (and how to avoid them)
- Mixing up the order. If the first ratio is "rice : water", the second must be too.
- Different units. Convert minutes to hours, or grams to kilograms, before comparing.
- Forgetting the whole. When sharing a total, remember the whole is the sum of all the parts.
- Dividing by zero. Some proportions have no answer if a zero ends up on the bottom. The calculator tells you when that happens.
- Over-rounding. We keep up to six decimal places, which is far more than most real-life problems need.
Frequently asked questions
How do you calculate a ratio?
Write the two quantities as A:B, then divide both by their greatest common divisor to reach the simplest form. For example, 12:18 divided by 6 becomes 2:3.
How do I find a missing number in a ratio?
Set up the proportion A:B = C:D and cross-multiply. If D is the unknown, D = (B × C) ÷ A. The first tab does this for any of the four positions and shows each step.
Can a ratio have decimals?
Yes. Multiply every number by 10, 100 or 1000 until they are all whole, then simplify as usual. The calculator does this automatically and tells you what it did.
What is the difference between a ratio and a fraction?
A ratio compares parts to each other (3:2), while a fraction compares a part to the whole (3/5). A 3:2 ratio means the whole is divided into 5 equal parts, 3 for one side and 2 for the other.
How do I split an amount using a ratio?
Add the ratio parts together, divide the total by that sum, then multiply by each part. Splitting 100 in the ratio 3:2 gives 60 and 40. Use the "Split an amount" tab to do it instantly.
How do I turn a ratio into a percentage?
Add all the parts to get the whole, divide each part by the whole and multiply by 100. A 2:3 ratio becomes 40% and 60%.
How do I find the aspect ratio of a screen or image?
Treat the width and height as a ratio and simplify it. A 1920 × 1080 screen simplifies to 16:9. To resize it, keep the proportion and cross-multiply to find the missing side.
What is the golden ratio?
The golden ratio is about 1.618. Two parts are in the golden ratio when the longer part divided by the shorter part equals 1.618, which is also the whole divided by the longer part.
Is this ratio calculator really free?
Yes. It is free with no limit on how many times you use it, needs no account, and runs in your browser so your numbers are never uploaded.