Use the calculator below to solve proportions of the form A/B = C/D. Enter three values and choose which unknown you want to find. The calculator shows the complete step-by-step cross-multiplication solution.
Cross-Multiplication Calculator
Enter three numbers
Fill in three of the four fields and select which value you want to calculate. Leave the unknown field blank.
How to use the calculator
- Fill in three fields (A, B, C, or D) with the known values and leave the unknown field blank.
- Select which variable you want to find from the dropdown menu.
- Click Calculate or press Enter to see the result.
- View the detailed step-by-step solution below the result.
Cross-Multiplication Formulas
| Unknown | Formula |
|---|---|
| A | A = (B × C) ÷ D |
| B | B = (A × D) ÷ C |
| C | C = (A × D) ÷ B |
| D | D = (B × C) ÷ A |
Frequently asked questions
What is cross-multiplication?
Cross-multiplication is a technique for solving proportions of the form A/B = C/D. The method involves multiplying diagonally: A × D = B × C. The unknown is then isolated by dividing both sides by its coefficient.
Example: To find D in 2/5 = 3/D, we apply 2 × D = 5 × 3, therefore D = 15 ÷ 2 = 7.5.
When should I use cross-multiplication?
Use cross-multiplication whenever you have a proportion equation with four terms and need to find one of them. Common applications include rule of three, map scales, recipes, currency conversion, and percentages.
Does cross-multiplication work with decimal numbers?
Yes. Cross-multiplication works with integers, decimals, and fractions. The calculator accepts a comma or period as the decimal separator. Just make sure no denominator is zero.
What is the difference between cross-multiplication and rule of three?
The rule of three is an application of cross-multiplication. In the rule of three, a table is organized with two proportional quantities and values are cross-multiplied to find the unknown. Every rule of three uses cross-multiplication, but cross-multiplication can be used in any proportion A/B = C/D.
Read also…
