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Ratio calculator
Simplify a ratio and find the missing number in an equal ratio.
Quick answer
Enter A and B to simplify the ratio, and C to find D so that A : B = C : D. The ratio 12 : 18 simplifies to 2 : 3, and 10 : 15 is equal to it.
Simplest ratio
2 : 3
- D, so that 12 : 18 = 10 : D
- 15.0000
- A รท B as a decimal
- 0.6667
How it works
A ratio compares two quantities. Dividing both by the same number does not change it, so 12 : 18 and 2 : 3 are the same ratio.
To scale a recipe or a map, keep the ratio and solve for the missing number.
Cross-multiplying is the shortcut: A ร D = B ร C.
The formula
- Simplify by dividing A and B by their greatest common divisor
- A : B = C : D gives D = C ร B รท A
A worked example
12 : 18: the greatest common divisor is 6, so the ratio is 2 : 3. If C = 10, then D = 10 ร 18 รท 12 = 15, so 12 : 18 = 10 : 15.
Common questions
How do I simplify a ratio?
Divide both numbers by their greatest common divisor. For 12 : 18 that is 6, giving 2 : 3.
How do I split an amount in a ratio?
Add the parts, divide the total by that sum and multiply by each part. โน500 in 2 : 3 is โน200 and โน300.
Can ratios use decimals?
Yes. The calculator scales decimals to whole numbers before simplifying.
What is a proportion?
A statement that two ratios are equal, such as 12 : 18 = 10 : 15.