Proportion Calculator

Solve any proportion a / b = c / d. Enter three values, leave one empty, and get the missing number with the cross-multiplication steps.

Solve a / b = c / d. Fill in any three values and leave the unknown one empty.

What is a proportion?

A proportion states that two ratios are equal: a / b = c / d. If you know three of the four numbers, you can always find the fourth. Proportions appear in scaling recipes, converting maps and drawings, calculating prices per unit, mixing solutions and solving percentage problems.

The formula and cross-multiplication

The rule is that the cross products are equal: a × d = b × c. From it you get each unknown directly:

a = (b × c) ÷ d
b = (a × d) ÷ c
c = (a × d) ÷ b
d = (b × c) ÷ a

Worked examples

Scaling a recipe: 3 cups of flour make 4 servings. How many cups for 12 servings? 3 / 4 = x / 12, so x = 3 × 12 ÷ 4 = 9 cups.
Unit price: 5 notebooks cost 12.50. How much do 8 cost? 5 / 12.50 = 8 / x, so x = 12.50 × 8 ÷ 5 = 20.00.
Map scale: 2 cm on the map equal 15 km. What distance is 7 cm? 2 / 15 = 7 / x, so x = 15 × 7 ÷ 2 = 52.5 km.

Direct and inverse proportion

This calculator solves direct proportions, where both quantities grow together, such as price and quantity. In an inverse proportion, one quantity grows while the other falls, for example speed and travel time. For those cases, use the relation a × b = c × d instead: if 4 workers need 6 days, how long do 8 workers need? 4 × 6 = 8 × x, so x = 3 days.

How to use the proportion calculator

Enter three of the four values a, b, c and d.
Leave the unknown field empty.
Press Solve proportion to see the missing value, the cross-multiplication and the simplified ratio.

Frequently asked questions

How do you solve a proportion?

Cross-multiply. For a / b = c / d, the product a × d equals b × c. Isolate the unknown: for example c = (a × d) ÷ b.

What is the difference between a ratio and a proportion?

A ratio compares two quantities, like 3 : 4. A proportion says that two ratios are equal, like 3 / 4 = 9 / 12.

Can I use decimals or negative numbers?

Yes. The calculator accepts decimals and negative values. The only restriction is that the denominators b and d cannot be zero.

How do I use it for percentages?

Write the percentage as a proportion with 100. To find 15 percent of 80, solve 15 / 100 = x / 80, which gives x = 12.

What is the rule of three?

It is another name for solving a proportion with three known values to find the fourth. The simple direct rule of three is exactly a / b = c / d.

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