Cross multiplication is the quick way to solve proportions: scaling recipes, converting units, using map scales or finding missing sides of similar triangles. If 3 cups of flour make 12 cookies, 3/12 = x/40 tells you how much flour 40 cookies need.
How to use the Cross Multiplication Calculator
- Unknown value
- A
- B
- C
- D
Results update as you type, and everything is calculated in your browser.
How it works
Multiply diagonally across the equals sign and divide by the remaining number. Choose which value is unknown; its field is hidden and calculated.
Tips
- Estimate the answer first so you can spot an impossible result.
- Work with whole numbers where possible and place the decimal point at the end.
- Use the order of operations: brackets, powers, multiplication and division, then addition and subtraction.
- For large integers, the calculator works with exact whole-number arithmetic in your browser.
Common mistakes to avoid
- Misaligning decimal points when adding or subtracting.
- Forgetting the remainder in whole-number division.
- Rounding too early in a multi-step calculation.
Inputs explained
| Field | What to enter |
|---|---|
| Unknown value | Choose one: A, B, C, D |
| A | A number |
| B | A number |
| C | A number |
| D | A number |
Example values
How the main result changes when A changes and everything else stays at the example values above:
| A | Missing value |
|---|---|
| 1.5 | 80 |
| 2.25 | 53.3333 |
| 3 | 40 |
| 3.75 | 32 |
| 4.5 | 26.6667 |
| 6 | 20 |
Formula
A/B = C/D ⇔ A·D = B·C
A = B·C/D, B = A·D/C, C = A·D/B, D = B·C/A
Worked example
Inputs — Unknown value: D; A: 3; B: 12; C: 10.
Results — Missing value = 40; Common ratio = 0.25.
Key terms
- Proportion
- An equation stating that two ratios are equal.
Frequently asked questions
How does cross multiplication work?
In A/B = C/D, multiplying both sides by B·D gives A·D = B·C.
Can I use it for 3/4 = x/20?
Yes: 4x = 60, so x = 15.
What if a denominator is zero?
The proportion is undefined; denominators must be non-zero.
Is it the same as the rule of three?
Yes – the rule of three is cross multiplication applied to proportions.
What formula does the Cross Multiplication Calculator use?
A/B = C/D ⇔ A·D = B·C.