Proportion Calculator

Use this calculator to easily solve proportion equations. Enter any three numbers in the denominator and enumerator for the two proportions and the fourth will be calculated for you.

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What is a proportion?

From mathematics, a proportion is simply two ratios in an equation, for example 1/2 = 50/100, 75/100 = 3/4, 9/10 = 90/100. If one variable is a product of the other variable and a constant, the two variables are called directly proportional - in this case x/y is a constant ratio. If the product of two variables is a constant, the two are inversely proportional - in this case xy is a constant.

Proportions are used in problems involving changing numbers while keeping a ratio constant. For example, if the price of a hamburger has risen by 10%, you might express this as a proportion: old price / 100 = new price / 110, so if you know the old price you can solve the proportion equation to find the new price. If the old price was $5, then $5/100 = x/110, then x = $5 / 100 * 110 = $5.5. While you can certainly do such calculations using our proportions calculator above, percentage math is easier using our percent calculator.

Proportions are also often used in unit conversion, where the difference between units of the imperial and metric system are proportionally constant. Scaling and resizing often require the calculation of proportions, such as if you know the desired width of an image, photo or video, you can figure out the required height to preserve the aspect ratio. Similarly, to read distances on a map you need to be able to solve proportions.

How to solve proportions?

Solving proportional equations is fairly trivial, if you know the basic equation transformation laws - multiplying and dividing both sides by the same number is all that is required. Of course, with the help of our proportion calculator all the work is done for you.

Example calculation

Say you have the proportion 4/5 = 12/x and need to find x. To solve for x, you need to first multiply both sides by x, resulting in x · 4/5 = 12. Then you divide both sides by 4/5, getting x = 12 / (4 / 5) = 12 / 4 * 5 = 3 * 5 = 15. Therefore, 4 is to 5 as 12 is to 15.

Cite this calculator & page

If you'd like to cite this online calculator resource and information as provided on the page, you can use the following citation:
Georgiev G.Z., "Proportion Calculator", [online] Available at: URL [Accessed Date: 31 Mar, 2020].