Cross Multiplication Calculator
Use the proportion format a / b = c / d. Enter any three values and leave exactly one box blank to solve for the missing number.
What is cross multiplication?
Cross multiplication is a quick method for solving proportions. A proportion is an equation showing that two ratios are equal, such as:
a / b = c / d
If the proportion is true, then the cross products are equal:
a × d = b × c
This lets you solve for an unknown value without converting everything into decimals first.
How to use this calculator
- Enter values for three fields in the proportion a / b = c / d.
- Leave one field blank (that is the unknown).
- Click Calculate.
- The calculator solves the missing value and shows the cross-multiplication step.
If you enter all four numbers, the calculator will check whether the proportion is true by comparing both cross products.
Why this method works
Suppose you have:
3 / 5 = x / 20
Cross multiply:
3 × 20 = 5 × x → 60 = 5x → x = 12
The calculator automates this process, including decimal handling and input validation.
Practical uses of cross multiplication
1) Unit conversions
If 1 inch = 2.54 cm, then 5 inches corresponds to how many centimeters? Set up a proportion and solve.
2) Recipe scaling
If a recipe needs 2 cups of flour for 12 cookies, how much for 30 cookies? Proportions make scaling easy.
3) Map and model scale problems
When you know one scale relationship, cross multiplication helps find real-world distances quickly.
4) Financial and rate problems
Hourly pay, interest approximations, and cost-per-unit comparisons often reduce to proportion equations.
Common mistakes to avoid
- Leaving more than one field blank: a single proportion needs exactly one unknown for a unique solution.
- Using zero as a denominator: denominator values (b or d) cannot be zero.
- Crossing incorrectly: multiply diagonal pairs, not top-to-top or bottom-to-bottom.
- Rounding too early: keep precision through intermediate steps when possible.
Quick examples
Example A
7 / 9 = x / 27
7 × 27 = 9x → 189 = 9x → x = 21
Example B
x / 4 = 10 / 5
x × 5 = 4 × 10 → 5x = 40 → x = 8
FAQ
Can I use decimals or negative numbers?
Yes. The calculator accepts integers, decimals, and negative values.
What if all four fields are filled?
It checks whether the two ratios are equal by comparing cross products.
What if no unique solution exists?
If the algebra would require division by zero (for example, solving with a zero divisor), the calculator shows an error message.