Cross-Multiply Calculator
The rule of three is the everyday workhorse for scaling: if three numbers in a proportion are known, cross-multiplying finds the fourth. It is how you scale a recipe from four servings to six, convert a map distance to real miles, work out a price for a different quantity, or read a unit rate off a label. This calculator solves a / b = c / x for the unknown x in one step, so you never have to rearrange the equation by hand.
Calculate
Default result: 12.0000
Cross-Multiply Calculator · Result
calculators.dev
x (the missing term)
3 × 4 × 9
Reviewed by the calculators.dev team · Last updated 2026-06-23
How to calculate
Picture your problem as two equal fractions, a / b = c / x, where x is the value you want. Enter the three numbers you know in their positions: a top-left, b bottom-left, and c top-right. The calculator cross-multiplies — multiplying along each diagonal — to get a × x = b × c, then divides to isolate x = (b × c) ÷ a. For 3 / 4 = 9 / x the answer is (4 × 9) ÷ 3 = 12. Change any term and x recalculates instantly.
Starting from a / b = c / x, cross-multiplication multiplies each numerator by the opposite denominator to clear the fractions: a × x = b × c. Solving for the unknown gives x = (b × c) ÷ a. The method works because two equal fractions stay equal when both sides are multiplied by the same product of denominators.
Example calculation
To solve 3/4 = 9/x, cross-multiply: the product of the top-left and bottom-right equals the product of the bottom-left and top-right, so 3 × x = 4 × 9. That gives 3x = 36, and dividing both sides by 3 leaves x = 12. The rule of three names this exactly: three known terms always pin down the fourth.
- solvedX
- 12
Assumptions
- The unknown x sits in the bottom-right position; rearrange your proportion so the value you want is there before entering the numbers.
- The top-left term a divides the answer, so it cannot be zero — a zero there would mean dividing by nothing.
- All four positions must describe the same kind of comparison (for example miles to hours on both sides), or the proportion is not valid.
Common mistakes
- Multiplying straight across (a × b = c × x) instead of along the diagonals, which gives the wrong equation.
- Putting the known and unknown in mismatched positions, so the units no longer line up on both sides.
- Setting up the proportion with the comparison reversed on one side, such as hours-to-miles against miles-to-hours.
Frequently asked questions
How does cross-multiplication solve for x?
From a / b = c / x it produces a × x = b × c by multiplying along the diagonals, then divides by a to give x = (b × c) ÷ a.
What is the rule of three?
A method for finding an unknown fourth term when three terms of a proportion are known. It is exactly what cross-multiplying a / b = c / x does.
When would I use this in real life?
Any time you scale: adjusting a recipe, converting a map scale, pricing a different quantity, or finding a rate from a sample.
Why must the top-left number not be zero?
Solving for x divides by the top-left term. Dividing by zero is undefined, so the calculator asks for a non-zero value instead.