Ratio Calculator
Simplify ratios to their lowest terms, find equivalent ratios, and solve for missing values. Enter the ratio parts below and choose your operation.
Frequently Asked Questions
Divide both parts of the ratio by their Greatest Common Divisor (GCD). For 12:8, GCD is 4, so 12÷4 : 8÷4 = 3:2.
Cross-multiply: if A:B = C:D, then A×D = B×C. So D = (B×C)/A. Example: 3:4 = 9:D → D = (4×9)/3 = 12.
What a ratio expresses
A ratio compares two quantities. Writing 3:2 says that for every 3 of the first thing there are 2 of the second — it describes the relationship, not the absolute amounts. 3:2, 6:4 and 300:200 are all the same ratio.
Simplifying
Divide both sides by their greatest common divisor.
Example: 12:18. The largest number dividing both is 6, so 12 ÷ 6 = 2 and 18 ÷ 6 = 3, giving 2:3.
A ratio is in simplest form when no whole number above 1 divides both sides evenly.
Solving for a missing value
Equivalent ratios are solved by cross multiplication.
Example: a recipe serving 4 uses 300g flour. For 10 servings:
4 : 300 = 10 : x, so x = (300 × 10) ÷ 4 = 750g
Part-to-part vs part-to-whole
This distinction causes more confusion than anything else about ratios.
If a class has a boys-to-girls ratio of 3:2, that is part-to-part. The total is 3 + 2 = 5 parts, so boys are 3/5 of the class (60%), not 3/4.
Mixing the two up is the classic error. Always check whether the second number is the other part or the whole.
Splitting a total by a ratio
To divide $4,500 between three people in the ratio 4:3:2:
- Total parts: 4 + 3 + 2 = 9
- One part: $4,500 ÷ 9 = $500
- Shares: $2,000, $1,500 and $1,000
Where ratios come up
Scaling recipes up or down, mixing concrete or fuel, map and model scales, aspect ratios for screens and images, financial ratios like debt-to-income, and splitting costs or profits between partners.