Use the calculator to solve a missing value in A / B = C / D. Below, you can see the formula, the cross-multiplication method, and worked examples.
How to solve proportions
The fastest way to solve a proportion is cross multiplication. If two ratios are equal, then the product of the left numerator and right denominator equals the product of the right numerator and left denominator.
For example, suppose you need to solve:
- Cross multiply: 12x = 96 x 7.
- Multiply the known values: 12x = 672.
- Divide both sides by 12: x = 56.
The calculator on this page uses the same cross-multiplication process and shows the step-by-step solution after you enter three values.
Proportion formula
A proportion compares two equal ratios. In this calculator, the proportion is written as:
If one value is missing, rearrange the cross-multiplication equation to solve for that value:
Fill in any three values, choose the missing letter in the calculator, and it will apply the matching formula.
Proportion examples
Proportions show up whenever one quantity scales with another. Here are a few common examples:
Solving for a missing denominator
If 4 / 5 = 24 / x, cross multiply:
Recipe scaling
If a recipe uses 2 cups of flour for 8 servings, you can set up a proportion to find the flour needed for 20 servings.
Map scale
If 1 inch on a map represents 5 miles, then 3.5 inches represents 17.5 miles.
Unit price
If 6 items cost $18, a proportion can help you find the cost of 10 items at the same rate.
Practice proportion problems
Try these practice problems after using the calculator. Each one uses the same cross-multiplication method shown above.
Missing denominator
Solve for the missing denominator
4 / 5 = 24 / x
Show answer
x = 30
Missing numerator
Solve for the missing numerator
x / 12 = 21 / 36
Show answer
x = 7
Equivalent ratios
Scale an equivalent ratio
7 / 12 = x / 96
Show answer
x = 56
Word problems
Recipe scaling
2 cups / 8 servings = x cups / 20 servings
Show answer
x = 5 cups
Want more practice? Visit the full proportion examples page for more problems with step-by-step answers.
What is a proportion?
If you need a quick refresher, a proportion is an equation stating that two ratios are equal. A ratio can be written as a fraction, with a colon, or sometimes as a decimal or percent.
For example, 7 / 12 and 56 / 96 are proportional because both describe the same relationship after scaling.
The numerator is the top number of a fraction, and the denominator is the bottom number. When a proportion has one missing value, cross multiplication lets you solve it.
Constant of proportionality
The constant of proportionality is the fixed relationship between two quantities. If two variables are directly proportional, their ratio stays the same:
Speed is a familiar example. If distance and time increase at the same rate, velocity is the constant ratio:
Here, v is velocity, s is distance, and t is time.
Direct and inverse proportion
In a direct proportion, both values increase or decrease together while their ratio stays constant.
In an inverse proportion, one value increases while the other decreases, and their product stays constant.
For a fixed distance, speed and travel time are inversely proportional: a higher speed means a shorter travel time.
The golden ratio
The golden ratio is a special proportional relationship often seen in geometry, design, and architecture. Given two quantities aand b, the golden ratio is written as:
Its value is approximately 1.618. It is not usually the first thing you need for solving a missing value, but it is a useful example of how proportional relationships appear outside basic arithmetic.
In geometry, proportions are also used with similar polygons. Two polygons are similar when their corresponding sides are in proportion.