Proportion
Equality of two ratios.
What does Proportion mean?
A proportion is a mathematical statement that two ratios are equal. It takes the form a/b = c/d, meaning the relationship between a and b is the same as between c and d. Proportions are used extensively in scaling recipes, converting units, resizing images, map reading, and solving real-world problems where quantities change at constant rates.
How to calculate Proportion
To solve a proportion a/b = c/d for the unknown d, cross-multiply and divide: d = (b × c) / a. For example, if 3/6 = 5/d, then d = (6 × 5) / 3 = 10. You can verify the result by checking that both ratios simplify to the same value — here 3/6 = 0.5 and 5/10 = 0.5.
FAQ
A ratio is a comparison of two quantities (e.g., 3:6), while a proportion is an equation stating that two ratios are equal (e.g., 3/6 = 5/10). A ratio describes a single relationship; a proportion links two relationships together.
Given a/b = c/d, cross-multiplication means multiplying across the equals sign diagonally: a × d = b × c. Then solve for the unknown by dividing both sides. For example, to find d: d = (b × c) / a.
Yes. Proportions work with any real numbers including decimals, fractions, and negative numbers. The principle is the same — cross-multiply and divide to find the unknown value.
Proportions are used in cooking (scaling recipes), map reading (converting scale distances to real distances), photography (resizing images while keeping aspect ratio), currency conversion, unit conversion, and many science and engineering applications.
If A is zero, the proportion a/b = c/d is undefined because division by zero is not allowed. The calculator requires A to be a positive number to produce a valid result.
Related calculators
- Ratio— Relative comparison of values.
- Percentage Change— Relative increase or decrease.
- Factorial— Product of descending integers.