Ratio and Proportion Calculator

What are ratio and proportion?

A ratio compares two quantities of the same kind by division. A proportion states that two ratios are equal. When three of the four numbers in a proportion are known, the fourth follows.

Direct proportion

Two quantities are in direct proportion when one grows at the same rate as the other. Amount of material and price, or distance and time at constant speed, behave this way. The rule is a / b = c / x, so x = b × c / a. This is cross multiplication, also known as the rule of three.

Example: if 5 kg of paint costs 40, then 8 kg costs 40 × 8 / 5 = 64.

Inverse proportion

Two quantities are in inverse proportion when one shrinks at the same rate as the other grows. Crew size and job duration, or speed and travel time over the same distance, behave this way. The rule is a × b = c × x, so x = a × b / c.

Example: a job that takes 6 workers 10 days takes 4 workers 6 × 10 / 4 = 15 days.

Splitting in a ratio

To split a quantity in a ratio such as 1 : 2 : 3, add the ratio terms, divide the quantity by that sum and multiply by each term. Splitting 600 units as 1 : 2 : 3 gives 100, 200 and 300. Mortar and concrete mix proportions work the same way.

Limits

The calculator assumes the relationship is exactly proportional. You decide first whether it is direct or inverse: choosing the wrong type gives the wrong answer.