How to use the ratio calculator
- To solve a proportion, fill in three of the four boxes in A : B = C : D and leave the unknown one blank.
- To simplify a ratio, fill in only A and B. The calculator reduces it to lowest terms and shows it as 1 : n, a decimal and a percentage split.
- Use the scale table to multiply the ratio up, for example to double a recipe or enlarge a drawing.
How to solve a proportion
Two ratios are in proportion when they describe the same relationship, so A ÷ B = C ÷ D. Multiplying across (cross-multiplying) gives A × D = B × C, and you can rearrange that to find any missing value:
Solve 3 : 4 = x : 20.
x = 3 × 20 ÷ 4 = 60 ÷ 4 = 15. Check: 3 ÷ 4 = 0.75 and 15 ÷ 20 = 0.75.
How to simplify a ratio
Divide both numbers by their greatest common divisor (GCD), the largest number that divides both evenly.
Simplify 24 : 36. The GCD of 24 and 36 is 12, so 24 ÷ 12 : 36 ÷ 12 = 2 : 3.
For decimals, multiply both sides by 10, 100 or 1,000 until they are whole numbers, then simplify. 1.5 : 2.5 becomes 15 : 25, which simplifies to 3 : 5.
Common ratios
| Use | Ratio | What it means |
|---|---|---|
| Widescreen TV and video | 16 : 9 | 1920 × 1080, 3840 × 2160 |
| Classic photos and iPad | 4 : 3 | 1024 × 768 |
| 35mm photo prints | 3 : 2 | 6 × 4 in, 1.5 : 1 |
| Rice to water | 1 : 2 | 1 cup rice, 2 cups water |
| Golden ratio | 1 : 1.618 | Used in design and art |
| Concrete mix | 1 : 2 : 3 | Cement : sand : gravel |
Turning a ratio into percentages
To split a total in the ratio A : B, add the parts and divide each by the sum. A 3 : 2 split gives 3 ÷ 5 = 60% and 2 ÷ 5 = 40%. To share $500 in a 3 : 2 ratio, one person gets $300 and the other $200.
For other percentage questions, the tip calculator handles splitting a bill between people.
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 simplify. 10 boys and 15 girls is 10 : 15, which simplifies to 2 : 3.
How do I find the missing number in a ratio?
Cross-multiply and divide. For A : B = C : x, the missing value is x = B × C ÷ A. For 2 : 5 = 6 : x, x = 5 × 6 ÷ 2 = 15.
Can a ratio have decimals?
Yes. The calculator accepts decimals. To simplify one by hand, multiply both sides by a power of 10 until they are whole numbers, then divide by the greatest common divisor.
What is the difference between a ratio and a fraction?
A ratio compares one part to another part, while a fraction compares a part to the whole. A 2 : 3 ratio of red to blue means red is 2/5 of the total, not 2/3.
How do I calculate an aspect ratio?
Divide width and height by their greatest common divisor. 1920 × 1080 has a GCD of 120, giving 16 : 9. To find a missing dimension, enter 16 : 9 = width : blank.