Proportion Calculator
Solve for any missing term in a/b = c/d.
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. When one of the four terms is missing — usually written as x — you can always recover it from the other three, because equal ratios have equal cross products. This calculator lets you choose which term (A, B, C or D) is the unknown, so it works whichever position x sits in. 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
Cross-multiply a/b = c/d into a × d = b × c, then divide by the term next to your unknown. Solving for d gives d = (b × c) / a; solving for a gives a = (b × c) / d; solving for b gives b = (a × d) / c; solving for c gives c = (a × d) / b. For example, in 3/6 = 5/x the unknown sits in the d position, so x = (6 × 5) / 3 = 10. Verify the answer by checking that both ratios simplify to the same value — here 3/6 = 0.5 and 5/10 = 0.5. The calculator prints this cross-multiplication step with your own numbers substituted so you can copy the working, not just the answer.
FAQ
Write the proportion so the unknown is one of the four terms, for example 3/6 = 5/x. Cross-multiply to get 3 × x = 6 × 5, then divide both sides by the number next to x: x = (6 × 5) / 3 = 10. Above, pick A, B, C or D as the unknown, enter the other three values, and the calculator shows the same cross-multiplication step with your numbers filled in.
The missing value is always the product of the two terms diagonally opposite each other, divided by the remaining term. Solving for D gives D = (B × C) / A, solving for A gives A = (B × C) / D, solving for B gives B = (A × D) / C, and solving for C gives C = (A × D) / B. That is the same rule in all four cases, because equal ratios have equal cross products.
Put the known conversion rate on one side and the value you are converting on the other, keeping the units in the same position on both sides. For example, 1 inch is 2.54 cm, so to convert 7 inches set up 1/2.54 = 7/x, giving x = (2.54 × 7) / 1 = 17.78 cm. Map scales, currency rates, recipe scaling and fuel-consumption figures all work the same way.
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 isolate the unknown by dividing both sides by whichever known term multiplies it. 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.
Only the term you divide by causes a problem. Solving for D divides by A, solving for A divides by D, solving for B divides by C, and solving for C divides by B — so that one term must not be zero, and the calculator flags it if you enter 0 there. Zeros in the other positions are fine and simply make the unknown zero too.
Related calculators
- Ratio— Relative comparison of values.
- Percentage Change— Relative increase, decrease or year-over-year change.
- Unit Conversion— Change measurement units.
- Factorial— Product of descending integers.