How to use the ratio calculator
- Simplify: type a ratio such as 1920:1080 or 12 18 30. Decimals are fine. The tool reduces it to the smallest whole numbers and shows each step.
- Solve for the missing value: enter three of the four numbers in A : B = C : D and leave the fourth empty. The tool works out the missing number by cross-multiplying.
- Split an amount: enter a total and a ratio, such as 500 and 2:3, to share the total in proportion.
Each tab shows the working so you can follow the method and check homework or a recipe by hand.
What a ratio is
A ratio compares quantities of the same kind. The ratio 2:3 says that for every 2 parts of the first thing there are 3 parts of the second. It can be written with a colon (2:3), as a fraction (2/3) or in words ("2 to 3"). Multiplying or dividing every term by the same number gives an equivalent ratio, so 2:3, 4:6 and 20:30 all describe the same proportion.
Simplify: divide every term by the greatest common divisor (GCD) Equal ratios: A : B = C : D ⇔ A × D = B × C Share of a total: part = total × term ÷ (sum of all terms)
When a ratio is first written with decimals, as in 1.5:2.5, the tool multiplies every term by a power of ten to make them whole numbers (15:25), then divides by the GCD (5) to get 3:5.
Worked examples
- Screen shape. 1920 : 1080. The GCD of 1920 and 1080 is 120. Dividing both gives 16 : 9, the standard widescreen ratio.
- Three terms. 12 : 18 : 30 has a GCD of 6, giving 2 : 3 : 5. The shares are 20%, 30% and 50%.
- Solve a proportion. 3 : 4 = 9 : x. Cross-multiply: 3 × x = 4 × 9 = 36, so x = 12.
- Scale a recipe. A dough uses flour to water at 5 : 3. With 750 g of flour, water = 3 × 750 ÷ 5 = 450 g.
- Share money. Split 500 in the ratio 2 : 3. There are 2 + 3 = 5 parts, so one part is 100. The shares are 200 and 300.
Common ratios in everyday life
| Ratio | Where it appears | Meaning |
|---|---|---|
| 16 : 9 | Video and monitors | Width is 1.78 times the height |
| 4 : 3 | Older TVs, many tablets | Width is 1.33 times the height |
| 3 : 2 | 35 mm photos | Width is 1.5 times the height |
| 1 : 1 | Square images | Equal sides |
| 1 : 50 000 | Map scales | 1 cm on the map is 500 m on the ground |
| 2 : 1 | Espresso to milk, or dough to water | Twice as much of the first |
| 1 : 1.618 | Golden ratio | The longer part is about 1.618 times the shorter |
Ratio versus fraction versus percentage
Ratios also scale. If a recipe for 4 people uses 2 cups of rice to 3 cups of water and you cook for 10, the multiplier is 10 ÷ 4 = 2.5, so you need 5 cups of rice and 7.5 cups of water. The ratio 2:3 stays the same, only the size of each part changes. The same idea drives map scales, paint mixes, concrete mixes and currency exchange.
A ratio of 2:3 compares one part to another part. As fractions of the whole, the parts are 2/5 and 3/5, or 40% and 60%. It is easy to confuse these: "2 out of 5" is a fraction of the whole (40%), but "2 to 3" is a part-to-part comparison. The sub-line in the result shows each term as a percentage of the total so you can move between the two views. A part-to-whole statement like "40% are girls" gives the ratio of girls to boys of 40:60, which simplifies to 2:3.
Accuracy and limits
Results are exact for whole-number ratios and for decimals with up to six places. Ratio terms must not be negative, and a ratio with a zero term, such as 0:5, simplifies to 0:1. The tool does not know the units you are comparing, so make sure both sides use the same unit (centimetres with centimetres) before you read the result. Rounded real-world measurements will not give exact simple ratios.
Frequently asked questions
How do I simplify a ratio?
Divide every term by their greatest common divisor. For 12:18, the GCD is 6, so the ratio is 2:3.
How do I find a missing value in a ratio?
Write the equation as A : B = C : D and cross-multiply, so A × D = B × C. Then divide to find the unknown. For 3:4 = 9:x, x = 4 × 9 ÷ 3 = 12.
What does a ratio of 1:3 mean as a percentage?
There are 4 parts in total, so the first part is 1/4 (25%) and the second is 3/4 (75%).
Can a ratio have decimals?
Yes. The tool multiplies by a power of ten to remove the decimals, simplifies, and shows the working. 1.5:2.5 becomes 3:5.
What is the difference between 2:3 and 3:2?
Order matters. 2:3 means the first quantity is smaller; 3:2 means it is larger. Swapping the terms inverts the ratio.