Ratio calculator
Simplify a ratio, or find the missing number in A : B = C : D.
About this calculator
This ratio calculator simplifies a ratio to its lowest terms, or finds the missing number in two equal ratios.
Use it to scale recipes, read map scales, mix paint or concrete, or resize images without stretching them.
How it works
A ratio is simplified by dividing both sides by their greatest common factor. In A : B = C : D, the missing D is C × B ÷ A, so both sides keep the same proportion.
Last reviewed:
Worked example
- Work out: A missing value
- A: 3
- B: 4
- C: 15
D: 20 (3 : 4 = 15 : 20)
Common questions
How do I simplify a ratio?
Divide both numbers by their greatest common factor. 12 : 18 becomes 2 : 3 after dividing both by 6.
How do I scale a recipe with ratios?
If a recipe for 4 uses 300 g of flour, for 6 people solve 4 : 300 = 6 : D, which gives 450 g.
What is the difference between a ratio and a fraction?
A ratio compares two parts, like 3 : 4, while a fraction compares a part with the whole. The ratio 3 : 4 means 3/7 and 4/7 of the total.
The story behind it
Where the idea came from: The ancient Greeks studied ratios closely, including the golden ratio of about 1.618 that appears in art, architecture and nature.
Euclid devoted a whole book of his Elements to ratio and proportion. The same idea now runs through cooking, maps, photography and engineering, anywhere one quantity needs to keep pace with another.
Why you can trust this calculator
- It runs in your browser. Nothing you type into it is sent anywhere.
- The method is explained on this page, so you can check it yourself.
- Free to use, with no sign-up.
- Results are estimates, so please double-check anything important.
- Spotted a mistake? Tell us and we'll look into it.
After 15 years as a mathematics educator, I built CalculStore to give students, teachers, professionals and anyone working with numbers simple, reliable tools.
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