Proportion calculator

How to solve a proportion

Enter the three numbers you know, and the field you leave empty is calculated automatically. The unknown can be anywhere: in a numerator or a denominator, on the left or on the right. When all four numbers are filled in, the calculator checks whether the proportion is true.

A proportion states that two ratios are equal: a/b = c/d, also written a : b = c : d. The terms a and d are called the extremes, and b and c the means. The fundamental property of proportions says that the product of the extremes equals the product of the means:

a/b = c/d  ⇔  a · d = b · c

This step is known as cross multiplication. From it you can solve for any unknown term:

Examples

Price of a larger quantity

3 lb of apples cost $12. How much do 5 lb cost? Proportion: 3/12 = 5/d, so d = (12 · 5) / 3 = $20.

Scaling a recipe

A recipe uses 2 cups of flour for 12 cookies. How much flour do you need for 30 cookies? Proportion: 2/12 = c/30, so c = (2 · 30) / 12 = 5 cups.

Map scale

On a 1 : 24,000 map, two points are 3 inches apart. What is the real distance? Proportion: 1/24000 = 3/d, so d = (24,000 · 3) / 1 = 72,000 inches, or 6,000 feet.

Unknown in the numerator

Proportion a/8 = 9/24: a = (8 · 9) / 24 = 3.

Frequently asked questions

How do I check whether a proportion is true?

Multiply the extremes and the means. The proportion is true when both products are equal. Once all four numbers are filled in, the calculator checks this itself and marks the fields green or red.

How do I calculate a different term?

Clear the field you want to find. The calculator always solves for the one field that is empty.

Can I enter decimals and fractions?

Yes. The calculator accepts decimals (2.5) and fractions written with a slash (3/4).

What is the difference between a ratio and a proportion?

A ratio compares two quantities, for example 3 : 12. A proportion states that two ratios are equal, for example 3 : 12 = 5 : 20.