A ratio compares two quantities, and a proportion says two ratios are equal. Learn what ratios and proportions are, how to simplify ratios, how to test whether two ratios are proportional, and how to solve a ratio and proportion problem for x — with a free calculator that shows every step.
Ratio and Proportion Calculator
Solve a/b = c/d — type x for the missing term.
Fractions like 3/4, mixed numbers like 1 1/2, decimals and negatives all work.
What Is a Ratio?
A ratio compares two numbers by division. The ratio 3 to 4 can be written as 3:4, as 3/4, or as “3 to 4”. Ratios describe parts of a whole, rates, and scales. In a class with 12 boys and 18 girls, the ratio of boys to girls is 12:18, which simplifies to 2:3. Order matters: boys to girls is not the same as girls to boys.
Ratio vs Proportion: What Is the Difference?
A ratio is one comparison, such as 2:3. A proportion is an equation of two ratios, such as 2/3 = 4/6. Every proportion contains two ratios, but a single ratio is not a proportion on its own. Use ratios to compare; use proportions to solve for an unknown value that keeps the comparison the same.
How to Simplify a Ratio
Divide both terms by their greatest common divisor. For 12:18, the greatest common divisor is 6, so 12 ÷ 6 = 2 and 18 ÷ 6 = 3, giving 2:3. For a ratio with decimals, first multiply both terms to clear the decimals: 1.5:2.5 becomes 15:25, then 3:5. Simplifying does not change the value of the ratio — it only writes it in lowest terms.
Equivalent Ratios and Unit Rates
Equivalent ratios are ratios with the same value: 2:3, 4:6, 6:9 and 10:15 are all equivalent. Multiply or divide both terms by the same number to get an equivalent ratio. A unit rate is a ratio with a denominator of 1, such as 60 miles per 1 hour, or $4.50 per 1 kilogram. Unit rates make it easy to compare prices and speeds.
Worked Examples
Example 1: Are 7/8 and 14/16 proportional? Cross products: 7 × 16 = 112 and 8 × 14 = 112. They match, so yes — it is a true proportion. Example 2: A paint mix uses 3 parts blue to 2 parts white. How much blue is needed for 10 parts white? Set 3/2 = x/10, cross-multiply: 2x = 30, x = 15 parts blue. Example 3: Simplify 45:60. The greatest common divisor is 15, so 45:60 = 3:4.
Ratio and Proportion FAQs
What is the difference between a ratio and a proportion?
A ratio compares two quantities, like 2:3. A proportion is an equation that says two ratios are equal, like 2/3 = 4/6.
How do you know if two ratios form a proportion?
Cross-multiply. If a × d equals b × c, the ratios form a proportion. For 7/8 and 14/16, both cross products are 112.
How do you solve a proportion for x?
Cross-multiply, then divide by the number next to x. In 3/4 = x/20, 4x = 60, so x = 15.
What is a unit rate?
A unit rate is a ratio with a denominator of 1, such as 60 miles per hour or $3 per kilogram. It is the best way to compare two prices or speeds.
Related tools: Proportion Calculator · Proportional Relationship · Percent Proportion · Math