How to use the ratio and proportion calculator
- Choose Solve a proportion, Simplify a ratio or Split a total by a ratio.
- To solve A : B = C : D, fill in three boxes and leave the one you want to find blank.
- To simplify, enter two numbers. Decimals are allowed.
- To split, enter the two ratio parts and the total.
Formula
Proportion: A / B = C / D, so A x D = B x C. For example D = B x C / A
Simplify: divide both numbers by their greatest common divisor
Split: part 1 = total x A / (A + B); part 2 = total x B / (A + B)
Decimals are scaled to whole numbers first by multiplying by 10, 100 and so on.
Worked examples
Proportion: 3 : 4 = 9 : D. D = 4 x 9 / 3 = 12.
Simplify: 1920 : 1080. Both divide by 120, giving 16 : 9, the familiar widescreen aspect ratio.
Split: share $250 in the ratio 2 : 3. Part 1 is 250 x 2 / 5 = 100 and part 2 is 250 x 3 / 5 = 150.
Scaling recipes and drawings
If a recipe uses 3 cups of flour for 4 servings, enter 3 : 4 = C : 10 to find the flour for 10 servings. The same method resizes images, maps and mixtures.
Aspect ratios and mixing ratios
Screens, photos and videos are described by aspect ratio. 1920 by 1080 simplifies to 16 : 9, and 1080 by 1080 is 1 : 1. Mixtures use ratios too: a 1 : 50 concentrate means 1 part product to 50 parts water, so one part is 1 / 51 of the total and 50 parts is 50 / 51.
Assumptions and limits
- In a proportion, exactly one box must be blank.
- Dividing by zero is blocked with an explanation.
- Ratio parts and totals must be zero or higher.
Frequently asked questions
What is the difference between a ratio and a proportion?
A ratio compares two quantities, such as 3 : 4. A proportion says two ratios are equal, such as 3 : 4 = 9 : 12.
How do I simplify a ratio?
Divide both numbers by the largest number that divides them evenly. 12 : 18 becomes 2 : 3.
How do I find the aspect ratio of a screen?
Enter the width and height in Simplify mode. 1920 x 1080 simplifies to 16 : 9.