Proportion Calculator
Solve a/b = c/x for the missing value.
Results update as you type.
How it works
A proportion is a statement that two ratios are equal, and solving a proportion means finding a missing value that makes both ratios match. This proportion calculator works with the proportion a over b equals c over x, taking the three known values a, b, and c and solving for the unknown x. The technique behind it is cross multiplication: when two fractions are equal, the product of the numerator of one and the denominator of the other equals the product of the other pair. Applying that to a over b equals c over x gives a times x equals b times c, and dividing both sides by a isolates x as b times c divided by a. For example, in the proportion 2 over 4 equals 3 over x, cross multiplying gives 2x equals 12, so x equals 6. Proportions are everywhere in practical mathematics. They power unit conversions, recipe scaling, map reading, and any situation where quantities keep a constant ratio. If a recipe serving four needs two cups of flour and you want to serve six, a proportion tells you how much flour to use. Similar triangles in geometry, currency exchange, and mixing ratios all rely on the same idea. This calculator requires the value a to be non-zero, because dividing by zero is undefined, which happens when the first term of the proportion is zero. Students, cooks, tradespeople, and designers all use proportions to scale quantities up or down while keeping relationships intact.
a/b = c/x ⟹ x = (b × c) ÷ a
A proportion states that two ratios are equal, so a divided by b equals c divided by x. Cross multiplying both sides, meaning multiplying each numerator by the opposite denominator, gives a times x equals b times c. Solving that for the unknown x divides both sides by a, producing x equals b times c divided by a. Cross multiplication works because multiplying both sides of an equation by the same non-zero quantities preserves the equality while clearing the fractions.
Source:Standard algebra
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Worked example
How to use this calculator
- 1
Enter your values
Enter a, b and c.
- 2
Adjust the options
Fine-tune any options to match your situation.
- 3
Read your result
x (missing value) updates instantly as you type — no button to press.
Frequently asked questions
What is a proportion?
A proportion is an equation stating that two ratios are equal, such as a over b equals c over d. It expresses that two pairs of quantities share the same relationship or scale. Proportions are used to compare quantities and to find an unknown value when three of the four terms are known. Solving them is one of the most useful everyday applications of algebra, from cooking to converting measurements.
What is cross multiplication?
Cross multiplication is the method used to solve a proportion. When two fractions are set equal, you multiply the numerator of each by the denominator of the other, producing an equation without fractions. For a over b equals c over x, cross multiplying gives a times x equals b times c. This works because multiplying both sides of the equation by the denominators preserves equality while clearing the fractions, making the unknown easy to isolate.
Where are proportions used in real life?
Proportions appear constantly in daily life. They scale recipes up or down, convert between units and currencies, read distances on maps, mix paint or chemicals in the right ratios, and calculate similar figures in geometry. Any time two quantities must stay in a fixed relationship as they grow or shrink, a proportion describes that link. They are among the most practical tools in everyday mathematics.
Why must the value a not be zero?
Solving the proportion for x requires dividing by a, and division by zero is undefined in mathematics. If a were zero, the ratio a over b would be zero, and there would be no consistent value of x to balance a non-zero ratio on the other side. The calculator therefore returns no result when a is zero. Rearrange the proportion so the unknown is not paired with a zero term.
How is a proportion different from a ratio?
A ratio compares two quantities, such as 2 to 4, showing their relative sizes. A proportion goes a step further by setting two ratios equal to each other, forming an equation like 2 over 4 equals 3 over 6. In short, a ratio is a single comparison, while a proportion states that two such comparisons are equivalent. Proportions let you solve for an unknown quantity that keeps the ratio constant.