Ratio Calculator
Simplify a ratio to lowest terms and solve a proportion for a missing value.
A ratio compares two quantities. To simplify one, divide both numbers by their greatest common divisor; 8:12 becomes 2:3. To solve a proportion where two ratios are equal, such as 2:3 = 10:?, cross-multiply: the missing value is 3 × 10 ÷ 2 = 15. Enter your numbers to simplify a ratio and solve for a missing term.
Results are estimates provided for general information.
Simplified ratio
2:3
- Simplified
- 2:3
- As a decimal (a ÷ b)
- 0.6667
- Solve 8:12 = 10:?
- 10 : 15
About the Ratio Calculator
A ratio shows how two quantities relate in size, written as a:b and read as “a to b.” Simplifying a ratio means reducing both sides to the smallest whole numbers that keep the same relationship, which you do by dividing each by their greatest common divisor. The ratio 8:12 and the ratio 2:3 describe the same proportion; the second is just easier to read. The other job this calculator handles is solving a proportion, where two ratios are set equal and one term is unknown, written a:b = c:?. You find the missing value by cross-multiplying, so 2:3 = 10:? gives 3 times 10 divided by 2, which is 15. Proportions appear whenever you scale something while keeping the parts balanced, such as adjusting a recipe, reading a map's scale, or mixing paint or fuel. The decimal form, a divided by b, is useful when you want the relationship as a single number.
Frequently asked questions
How do I simplify a ratio?+
Divide both numbers by their greatest common divisor. For 8:12 the greatest common divisor is 4, so the ratio simplifies to 2:3.
What is a proportion?+
A proportion is two equal ratios, such as 2:3 = 10:15. When one term is missing, you can solve for it by cross-multiplying.
How do I solve A:B = C:X?+
Multiply B by C and divide by A. For 2:3 = 10:X, X = 3 × 10 ÷ 2 = 15.
What is the difference between a ratio and a fraction?+
A ratio compares two separate quantities (a to b). A fraction expresses one number as a part of a whole. The ratio 2:3 corresponds to a part that is 2/5 of the total.