Solve a missing number in a proportion, or split a number by a ratio. Enter three numbers and leave one box blank, and the calculator will find the missing value. Everything runs in your browser; nothing you enter is uploaded.
Solve a proportion
Leave exactly one box blank. That blank box is the number the calculator will find.
Split a number by a ratio
For example, split 100 by 2:3 to get 40 and 60.
Worked example
Find the missing number in 3:4 = x:12. Multiply across the diagonal you know: 3 x 12 = 36. Then divide by the number left on the other side: 36 / 4 = 9. So x = 9, and 3:4 = 9:12.
To split 100 by 2:3, add the ratio parts: 2 + 3 = 5. Each part is worth 100 / 5 = 20. So the first share is 2 x 20 = 40 and the second share is 3 x 20 = 60.
How to use this calculator
- For a proportion, enter three of the four numbers and leave exactly one box blank.
- Click Solve proportion to find the missing number.
- To split a number, enter the number and both parts of the ratio, then click Split by ratio.
- Read the result and the working shown underneath it.
How it works
A proportion says two ratios are equal, for example 3:4 = 9:12. Cross-multiplication works in plain words like this: multiply the top-left number by the bottom-right number, and multiply the top-right number by the bottom-left number. In a true proportion, those two answers are the same. When one number is missing, multiply the two numbers that sit diagonally opposite each other, then divide by the one number left over. That gives you the missing number.
To split a number by a ratio, add the ratio parts together, divide the number by that total to find what one part is worth, then multiply by each part of the ratio.
Frequently asked questions
What is a proportion?
A proportion is a statement that two ratios are equal, such as 3:4 = 9:12. Both sides describe the same relationship, just with different-sized numbers.
What if I leave two boxes blank?
The calculator needs three numbers to find the fourth. If two boxes are blank, it will show a plain-words message asking you to fill in three numbers and leave exactly one box blank.
Can I use decimals?
Yes. You can enter whole numbers or decimals, and the result may be a decimal if the numbers do not divide exactly.
What does it mean to split a number by a ratio?
It means sharing a total in the same proportions as the ratio. Splitting 100 by 2:3 gives 40 and 60, because 40 and 60 are in the ratio 2:3 and add up to 100.
What is cross-multiplication?
Cross-multiplication is multiplying diagonally across a proportion. It lets you turn a proportion with one missing number into a simple multiplication and division.