Proportion Calculator

Which formula solves each position in the proportion a/b = c/d?

All four formulas come out of one rule, the cross product a × d = b × c, which holds whenever the two ratios have the same value. Rearranging that equality once per position gives four divisions, so the missing term is a product of two known values divided by the third.

b and d sit under the fraction bar, so the calculator refuses a zero typed into either one. It also refuses a zero that the algebra produces on its own, the case of 0/x = 3/4 where the cross product forces x to 0 and leaves the first ratio without a value.

How to calculate a proportion by hand

Multiply across the diagonal, then divide by the term facing the gap. Take 3/4 = 9/x as an example: cross multiplication rewrites it as 3 × x = 4 × 9, the known side comes to 36, then dividing 36 by the 3 facing x leaves x = 12. Those lines appear in that same order under the result, below the literal formula x = (b × c) ÷ a.

The method holds wherever the gap sits. x/5 = 8/20 leaves the first term open, where the known cross product is 5 × 8 = 40 and the divisor is the 20 sitting opposite it, which lands on x = 2. A gap in the second box behaves the same way, so 3/x = 9/12 multiplies 3 by 12 before dividing that 36 by the 9 facing it, ending at x = 4.

Nothing on the page asks which term to solve for. The calculator reads the empty box as the unknown and treats an x, a capital X or a question mark the same way. Two empty boxes stop it, since a proportion missing two terms has an unlimited number of answers.

How do you check whether a proportion is true?

Filling all four boxes leaves nothing to solve, so the page compares the two cross products and returns a verdict instead. 2/3 = 5/7 comes back false, with a × d at 14 against 15 for b × c, a gap of 1. The same line names the value that would settle it, d = 7.5 in place of the 7, which comes from (3 × 5) ÷ 2.

The calculator compares the two products with a small tolerance on decimals, which keeps binary rounding, the tiny error a computer makes while storing 0.1, from turning a true proportion into a false verdict. 0.1/0.3 = 1/3 comes back true even though 0.1 × 3 evaluates to 0.30000000000000004 in a browser and not to 0.3.

Which everyday problems are proportions?

Flour at 250 g for 4 servings becomes 250/4 = x/6 for a table of six. The 375 g that comes back holds the flour at 62.5 g per serving, a factor of 1.5 that every other quantity in the recipe follows too.

A wall drawn at 12 cm on a 1:50 plan reads 1/50 = 12/x, which puts the real wall at 600 cm. The rule of three taught at school is this same layout under another name.

Unit prices and currency amounts at a fixed rate fold into these same four boxes. Turning a single fraction into a decimal or adding two of them belongs to the fraction calculator, while reducing a ratio to its smallest whole numbers is the job of the ratio calculator.