Proportion Calculator
Enter any three terms of a proportion — the fourth is found by cross multiplication, with every step shown.
Fill in any three values and leave one empty — the calculator finds the missing term.
A proportion states that two ratios are equal: A is to B as C is to D, written A : B = C : D or A/B = C/D. Whenever you know three of the four terms, the fourth can be found by cross multiplication, also called the rule of three. Enter any three values in the fields above, leave the unknown one empty and press Solve — the calculator shows the missing term and the exact formula it used, so you can copy the working into homework or check your own calculation. If you fill in all four fields, it tells you whether the proportion is true.
Proportions are everywhere in daily life. Scaling a recipe: if 4 eggs serve 6 people, 4/6 = x/15 gives 10 eggs for 15 guests. Reading a map: on a 1 : 50,000 map, 1.2 km (120,000 cm) is 1 × 120,000 ÷ 50,000 = 2.4 cm. Percentages are proportions too: 25 is to 100 as x is to 360, so 25% of 360 is 90. The same method converts currencies at a fixed rate, adjusts dosages by weight, resizes images without distortion and splits costs in a fair ratio.
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How do you solve a proportion?
Use the fundamental property of proportions: the product of the extremes equals the product of the means, A × D = B × C. To find the unknown, multiply the two known terms that sit diagonally opposite each other and divide by the remaining one. For 3 : 5 = 9 : x, x = 5 × 9 ÷ 3 = 15.
What is cross multiplication?
Cross multiplication means multiplying across the equals sign diagonally: the numerator of each fraction by the denominator of the other. If A/B = C/D, then A × D = B × C. It turns a proportion into a simple equation with one unknown.
What is the rule of three?
The rule of three is the everyday name for solving a proportion when three values are known. It works for directly proportional quantities: if 3 notebooks cost 12, then 7 notebooks cost 12 × 7 ÷ 3 = 28.
Which field should I leave empty?
Any one of the four. The calculator detects which term is missing and uses the matching formula. If two or more fields are empty, it asks you to fill in exactly three values.
What happens if I fill in all four fields?
The calculator switches to checking mode and tells you whether A : B equals C : D, showing both ratios as decimals so you can see how far apart they are.
Can I use decimals and negative numbers?
Yes. You can type decimals with either a dot or a comma (2.5 or 2,5) and negative values with a minus sign. Spaces used as thousands separators are ignored.
Why do I get a division by zero error?
The unknown is found by dividing by one of the known terms. If that term is 0, the division is undefined and no proportion can be solved. The same applies to B or D in checking mode, since a ratio with a zero denominator does not exist.
What is the difference between direct and inverse proportion?
In a direct proportion both quantities grow together: twice the flour, twice the bread. In an inverse proportion one grows as the other shrinks: twice the workers, half the time. This calculator solves direct proportions; for an inverse one, swap the terms of one ratio before entering them.
How do I scale a recipe with this calculator?
Put the original quantity in A and the original number of servings in B, the new number of servings in D, and leave C empty. For 300 g of flour for 4 servings scaled to 10 servings, C = 300 × 10 ÷ 4 = 750 g.
How do I calculate a percentage with a proportion?
Write the percentage over 100 and the part over the whole: 25/100 = x/360. Leave x empty and the calculator returns 90. For the reverse question, what percentage is 90 of 360, leave A empty instead.