# Cross Multiplication Calculator

URL: https://speedycalculator.com/calculators/math/cross-multiplication/
Last updated: 2026-10-30

> The cross multiplication calculator solves A/B = C/D for whichever value is missing, using A × D = B × C.

## Inputs

- Unknown value
- A
- B
- C
- D

## Results

- Missing value
- Common ratio

## 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
```

## Explanation

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.

### Inputs explained

FieldWhat to enterUnknown valueChoose one: A, B, C, DAA numberBA numberCA numberDA number

### Example values

How the main result changes when **A** changes and everything else stays at the example values above:

AMissing value1.5802.2553.33333403.75324.526.6667620

## 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.

## FAQ

**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.


## Sources

- [OpenStax – Prealgebra 2e](https://openstax.org/details/books/prealgebra-2e)
- [OpenStax – Contemporary Mathematics](https://openstax.org/details/books/contemporary-mathematics)