Proportion Calculator

Fill in three of the four boxes, leave the one you want to find empty, and press Calculate. The answer appears in the empty box, with the steps below.

Proportion Calculator: A / B = C / D

How to solve a proportion with cross multiplication

A / B = C / D → A × D = B × C

Multiply diagonally across the equals sign, then divide by the number next to the unknown:

Missing A: A = B × C ÷ D
Missing B: B = A × D ÷ C
Missing C: C = A × D ÷ B
Missing D: D = B × C ÷ A

Worked examples

Scaling a recipe

A recipe uses 2 cups of flour for 12 cookies. For 30 cookies: 2/12 = x/30, so x = 2 × 30 ÷ 12 = 5 cups.

Map scale

On a map, 1 inch = 25 miles. Two towns 3.4 inches apart are 1/25 = 3.4/x, so x = 25 × 3.4 = 85 miles apart.

Unit price

If 3 pounds cost $7.47, then 5 pounds cost: 3/7.47 = 5/x, so x = 7.47 × 5 ÷ 3 = $12.45.

Resizing an image

A 1920 × 1080 image resized to 1280 pixels wide keeps its shape at 1920/1080 = 1280/x, so x = 1080 × 1280 ÷ 1920 = 720 pixels tall.

When proportions don't apply

Proportions assume a straight-line relationship: twice the input gives twice the output. That's not true for everything. Baking time doesn't double when you double a recipe. Bulk pricing breaks it too, and so does area, which grows with the square of length.

Frequently asked questions

How do you solve a proportion?

Cross-multiply and divide. In A/B = C/D, A × D = B × C. To find D, divide B × C by A. For 3/4 = 9/x: 3x = 36, so x = 12.

What is the difference between a ratio and a proportion?

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

How do I know if two ratios are proportional?

Cross-multiply. If A × D equals B × C, the ratios are proportional. 2/5 and 6/15 are proportional because 2 × 15 = 30 and 5 × 6 = 30.

Can a proportion have decimals or negative numbers?

Yes. Cross multiplication works the same for decimals, fractions and negative numbers. The only restriction is that the value you divide by cannot be zero.

Proportion Calculator