How to use the Ratio Calculator
Fill in three of the four boxes in a : b = c : d and leave one empty. The calculator cross multiplies and solves for the missing value.
Scaling a recipe
A recipe uses 3 cups of flour for 4 people and you are cooking for 10. Write 3 : 4 = x : 10. Cross multiplying gives 4x = 30, so x = 7.5 cups. The same steps work for doubling a paint mix, resizing a drawing or adjusting a dose by weight when the instructions say to.
Keeping an aspect ratio
To resize a 1920 by 1080 image to 1280 pixels wide without stretching it, write 1920 : 1080 = 1280 : x. Cross multiplying gives x = 1280 × 1080 ÷ 1920 = 720, so the new size is 1280 by 720. The same steps keep photos, videos and screen layouts in proportion.
Maps, scales and unit prices
On a 1 : 50,000 map, 4 cm on paper is 4 × 50,000 = 200,000 cm, or 2 km on the ground. Proportions also compare prices: if 750 g costs $4.50, then 1 kg at the same rate costs $6. When both pairs keep the same ratio, the two quantities are directly proportional.
Equivalent ratios and simplifying
Equivalent ratios describe the same relationship with different numbers. 2 : 3, 4 : 6 and 10 : 15 are all equivalent, because each pair is the first one multiplied by the same number. To simplify a ratio, divide both sides by their greatest common factor: 18 : 24 divided by 6 becomes 3 : 4.
Scale factor
The scale factor is the number you multiply by to get from one ratio to an equivalent one. Going from 3 : 4 to 7.5 : 10 uses a scale factor of 2.5. Builders, model makers and designers use the same idea when they enlarge or shrink a drawing so every measurement stays in proportion.
The formula
Cross-multiply: a × d = b × c
Examples
- 3 : 4 = 9 : ?
D = 12 3 ÷ 4 = 9 ÷ 12
- 2 : 5 = ? : 20
C = 8 2 ÷ 5 = 8 ÷ 20
- Scaling a recipe: 250 g for 4 people is ? g for 6 people
C = 375 250 ÷ 4 = 375 ÷ 6
Limitations and assumptions
Computed in your browser with standard double-precision arithmetic unless the page says otherwise. Very large or very small values may be rounded.
Frequently asked questions
How do I solve a proportion?
Cross-multiply: a × d = b × c, then divide to isolate the unknown.
What is a proportion?
An equation stating that two ratios are equal, such as 3/4 = 9/12.
When are two quantities directly proportional?
When their ratio stays constant: double one and the other doubles too.
Can I use decimals?
Yes. Leave exactly one field empty and the calculator returns the missing value.