Enter two values to get the simplified ratio
A ratio expresses the relationship between two quantities — how many times one value contains or is contained within another. The ratio 3:1 means the first value is three times the second. The ratio 1:4 means the first value is one quarter of the second.
Ratios are simplified by dividing both values by their greatest common divisor (GCD). The ratio 6:9 simplifies to 2:3 because the GCD of 6 and 9 is 3.
To simplify a ratio A:B, find the greatest common divisor of A and B, then divide both by it.
Example: simplify 24:36. The GCD of 24 and 36 is 12. 24 ÷ 12 = 2, 36 ÷ 12 = 3. Simplified ratio: 2:3.
| Original | Simplified | As fraction |
|---|---|---|
| 2:4 | 1:2 | 1/2 |
| 6:9 | 2:3 | 2/3 |
| 15:25 | 3:5 | 3/5 |
| 100:75 | 4:3 | 4/3 |
| 7:14 | 1:2 | 1/2 |
Cooking and recipes: A recipe calling for a 2:1 ratio of flour to butter means for every 200g of flour, use 100g of butter. Scaling the recipe up or down preserves the ratio.
Maps and scale models: A map scale of 1:50,000 means 1 cm on the map represents 50,000 cm (500 m) in reality. Architectural blueprints use scales like 1:100 or 1:20.
Finance: The price-to-earnings (P/E) ratio compares a company's share price to its earnings per share. A P/E of 20:1 means investors pay $20 for every $1 of earnings.
Mixing solutions: A 1:10 dilution means 1 part concentrate to 10 parts water. A 1:3 cement-to-sand mix means 1 bucket of cement for every 3 buckets of sand.
Aspect ratios: Screen and image dimensions are expressed as ratios. 16:9 is the standard widescreen format. 4:3 is the older TV format. 1:1 is square.
A ratio compares two values (3:4). A proportion states that two ratios are equal (3:4 = 6:8). A fraction expresses one value as part of a total (3/4 means 3 out of 4 parts). They are related concepts but used in different contexts — ratios compare parts to parts, fractions compare part to whole.
Find the greatest common divisor (GCD) of both numbers and divide both by it. To simplify 18:24, the GCD is 6. 18 ÷ 6 = 3, 24 ÷ 6 = 4. Simplified: 3:4.
The ratio of 3 to 5 is written as 3:5. It cannot be simplified further because 3 and 5 share no common divisors other than 1. As a fraction it is 3/5, or 0.6 as a decimal.
Multiply or divide both parts of the ratio by the same number. The ratio 2:3 is equivalent to 4:6, 6:9, 10:15, and so on. All represent the same relationship.
A ratio compares two separate quantities (2 parts blue to 3 parts red). A fraction expresses one quantity as part of a whole (2 out of 5 parts are blue). The ratio 2:3 and the fraction 2/5 describe the same mixture but from different perspectives.
Ratios are usually expressed as whole numbers, but decimal ratios are used in some contexts — fuel mixture ratios, gear ratios, and financial ratios often include decimals. This calculator simplifies to the lowest whole number ratio.