Introduction
A proportion is a statement that two ratios are equal. For example, 4/5 = 8/10 is a proportion because both fractions have the same value. When one number in a proportion is missing, you can use cross multiplication to find it. This is a skill used in cooking, map reading, scale drawings, and many real-world math problems.
This proportion calculator solves for any missing value in a proportion. Just enter three known numbers and leave the fourth blank or type a letter like x. The tool finds the unknown value instantly and shows you a full step-by-step solution so you can learn how the answer was found. You can view your result as a decimal or a fraction, copy it to your clipboard, or download it as a PDF.
How to Use Our Proportion Calculator
Enter three known values into the proportion equation and leave one field blank to find the missing number. The calculator will solve for the unknown, show the answer, and give you a full step-by-step solution.
Fields a, b, c, and d: Type a number into any three of the four fields. These fields form the proportion a/b = c/d. Leave the field you want to solve empty, or type a letter like x in it.
Show result as: Pick Decimal to see your answer as a decimal number, or pick Fraction to see it as a simplified fraction.
Calculate: Click this button to solve the proportion and see your result, worked solution, and cross-product chart.
Reset: Click this button to clear your entries and go back to the default example.
What Is a Proportion?
A proportion is a math statement that says two ratios are equal. A ratio compares two numbers, like 3 to 4. When you write two equal ratios side by side, you get a proportion. For example, 3/4 = 6/8 is a proportion because both fractions have the same value.
How Proportions Work
Every proportion has four numbers, often called a, b, c, and d. They follow this pattern:
a / b = c / d
If you know three of the four numbers, you can always solve for the missing one. The trick is called cross multiplication. You multiply across the equal sign in an "X" shape: a × d = b × c. Then you solve for the number you don't know by dividing.
A Simple Example
Say you know that 4/5 = 6/x. Cross multiply to get 4 × x = 5 × 6, which gives you 4x = 30. Divide both sides by 4, and x = 7.5. That means 4/5 and 6/7.5 are equal ratios.
Where Proportions Are Used
Proportions show up everywhere in daily life. You use them when you resize a recipe, read a map, calculate speed and distance, or figure out sale prices. If a store sells 3 apples for $2, you can set up a proportion to find the cost of 12 apples. Builders, nurses, artists, and scientists all rely on proportions to keep numbers in balance.
Tips to Remember
- A ratio compares two numbers. A proportion says two ratios are equal.
- Cross multiplication is the fastest way to solve for a missing value.
- The denominator (bottom number) of a fraction can never be zero, because you cannot divide by zero.
- You can check your answer by plugging it back in. If both sides of the equation match, your answer is correct.