Ratio and proportion calculator

Direct proportion

Use it when two quantities are directly proportional: if one doubles, so does the other. For example, the price and the amount of a product, or the ingredients and the number of servings of a recipe.

If A corresponds to B, then C corresponds to X = B × C ÷ A. If 3 lb of apples cost $7.50, 5 lb cost 7.50 × 5 ÷ 3 = $12.50. This method is also known as the rule of three, or cross-multiplication.

Inverse proportion

Use it when quantities are inversely proportional: if one doubles, the other halves. For example, the number of workers and the days a job takes, or speed and travel time.

If A corresponds to B, then C corresponds to X = A × B ÷ C. If 4 painters take 6 days, 3 painters take 4 × 6 ÷ 3 = 8 days.

Before calculating, ask yourself: if the first quantity goes up, does the second go up or down? If it goes up, it's direct; if it goes down, inverse. Choosing the wrong type is the most common mistake.

Percentages as proportions

A percentage is a direct proportion where one of the quantities is 100. To find what percent 45 is of 180: if 180 corresponds to 45, then 100 corresponds to 45 × 100 ÷ 180 = 25, that is, 25%. For these cases there's also the percentage calculator.

Simplifying a ratio

Simplifying a ratio means dividing both numbers by their greatest common divisor. A 1920 × 1080 pixel screen has a 16 : 9 aspect ratio, and 12 : 18 is the same as 2 : 3. If there are decimals, the calculator first turns them into whole numbers: 1.5 : 2.25 is 2 : 3.

You'll also see the ratio written as “n : 1” (16 : 9 ≈ 1.7778 : 1) and each part's share of the total, which is handy for splitting costs or mixing ingredients.