Solve a proportion A : B = C : ? for the missing value. Enter the three known terms.
Usage Tip
Scaling a recipe is a proportion: if 2 cups serves 4, then for 6 people solve 2 : 4 = x : 6.
Cross-multiply: unknown = B × C ÷ A
This is the basis of scaling recipes, maps, and models.
A cannot be zero, since the solution divides by A.
Proportions assume the relationship is linear.
A proportion says that two ratios are equal, so A is to B as C is to an unknown value. The missing value is found by cross multiplying: multiply B by C and divide by A. If 3 cups of flour make 24 cookies, the same ratio shows that 5 cups would make 40.
Proportions are used for scaling recipes, reading maps and drawings, converting currencies, and working out unit rates. They only work when the relationship is truly proportional, meaning that doubling one quantity doubles the other. Keep the terms in the same order on both sides, and make sure matching terms use the same units. A is also not allowed to be zero.
Worked example: If a recipe uses 3 cups for 4 servings, then for 10 servings you need x where 3 ÷ 4 = x ÷ 10. Cross-multiplying gives x = 3 × 10 ÷ 4 = 7.5 cups.
Common mistakes: Keep the same quantity in the same position on both sides of the ratio, and use the same unit for each. Swapping the order, such as servings on top on one side and cups on top on the other, gives the wrong answer.
Related: the Percentage Calculator and the Recipe Scaler.