Proportion Calculator — solve a : b = c : x

How it works

A proportion is a statement that two ratios are equal — a : b = c : x, read "a is to b as c is to x". Because a ratio is really a fraction, this is the same as the equation:

a / b = c / x

To solve for the unknown x, cross-multiply: multiply each numerator by the other side's denominator to get a·x = b·c, then divide by a:

x = b × c ÷ a

Cross-multiplication is just a shortcut for clearing the fractions — it turns the equal-ratios statement into a simple multiplication and division. This is the engine behind scaling recipes, reading map distances, converting units and resizing images while keeping shape.

Worked example

Solve 2 : 3 = 10 : x. Writing it as fractions, 2/3 = 10/x. Cross-multiply to get 2·x = 3·10 = 30, then divide by 2:

x = (3 × 10) ÷ 2 = 30 ÷ 2 = 15

So 2 : 3 = 10 : 15 — and you can check it: 2/3 and 10/15 both equal 0.667. Another example: doubling a recipe with 1 : 2 = 50 : x gives x = (2 × 50) ÷ 1 = 100.

Frequently asked questions

How do I solve a proportion?

Set the two ratios equal as fractions and cross-multiply. For a/b = c/x, that's a·x = b·c, so x = b·c ÷ a. Always pair the numbers correctly: the term diagonally opposite the unknown, times the one above it, divided by the remaining one.

What is cross-multiplication?

A shortcut for solving an equation of two equal fractions. Instead of finding a common denominator, you multiply each side's numerator by the other side's denominator: a/b = c/x becomes a·x = b·c. It works because multiplying both sides of the equation by b and by x clears both denominators at once.

How do I check my answer?

Put the value back and compare the two ratios as decimals — they should match. For 2 : 3 = 10 : 15, both 2÷3 and 10÷15 equal 0.667, so 15 is correct. Equivalently, check that the cross-products are equal: 2 × 15 = 30 and 3 × 10 = 30.

Where are proportions used in real life?

Everywhere quantities scale together: doubling or halving a recipe, converting between units, working out map or model distances from a scale, mixing solutions to a fixed strength, and resizing an image or layout without distorting it. Anytime "if this much gives that, how much gives...?" comes up, it's a proportion.

What if the first term is zero?

Then there's no solution — the formula divides by a, and dividing by zero is undefined. A proportion with a zero term (0 : b = c : x) can't be scaled sensibly, so the calculator returns no value in that case.

Does it matter which term is the unknown?

The relationship is the same, but rearrange the formula to isolate whichever term is missing. This calculator solves for the fourth term x in a : b = c : x; if your unknown is in a different position, relabel the terms so the missing one is last, or apply cross-multiplication and solve for it directly.