Cross Multiplication Calculator

Solve a proportion a/b = c/d for its missing term. Enter the three known values, pick which one is unknown, and cross multiply (a × d = b × c) to find it.

Quick Facts

Formula
a × d = b × c, for the proportion a/b = c/d
Multiply diagonally across the equals sign, then divide by the term next to the unknown to isolate it.
Requirement
The term next to the unknown can't be zero
Isolating the unknown means dividing by that term, so a zero there makes the proportion unsolvable.

Your Results

Calculated
Unknown value (solved)
-
Missing term of the proportion
Cross product A × D
-
Left-hand diagonal product
Cross product B × C
-
Right-hand diagonal product (should match A × D)
Equivalent ratio (A ÷ B)
-
Decimal form of both sides of the proportion

Ready

Enter the three known terms of the proportion and choose which one to solve for.

How Cross Multiplication Works

Cross multiplication is the standard algebraic method for solving a proportion — an equation stating that two ratios are equal, written as a/b = c/d. Multiplying both sides by the two denominators clears the fractions and leaves a × d = b × c. Because three of the four terms are usually known in a real problem, you can rearrange that equation to solve for whichever one is missing.

Formula and method

Starting from a/b = c/d, cross multiplication gives a × d = b × c. Solving for each term individually:

  • a = (b × c) ÷ d
  • b = (a × d) ÷ c
  • c = (a × d) ÷ b
  • d = (b × c) ÷ a

Pick the term you don't know, enter the other three, and the calculator divides the product of the diagonal pair by the remaining known term.

Common sources of error

  • Mismatched order: a/b must correspond to c/d in the same order — swapping the numerator and denominator on one side breaks the proportion
  • Dividing by zero: the term next to the unknown can't be zero, since isolating the unknown requires dividing by it
  • Unit mismatch: both ratios should compare the same kind of quantity in the same units (for example, miles/hour on both sides), or the proportion has no real-world meaning

Checking your result

After solving, multiply the two diagonal pairs — a×d and b×c — and confirm they're equal. If they match, the proportion holds and your answer is correct. If they don't, recheck which term you solved for and whether the other three values are in the right positions.

Applications

Cross multiplication turns up anywhere two ratios need to stay equal: converting units (5 miles is to 8 kilometers as 20 miles is to how many kilometers?), scaling a recipe, resizing an image proportionally, or solving similar-triangle side lengths in geometry. In every case, three measurements are known and the fourth is found by cross multiplying and dividing.

Frequently Asked Questions

What is cross multiplication?
Cross multiplication is a technique for solving a proportion a/b = c/d by multiplying diagonally across the equals sign: a × d = b × c. Once three of the four terms are known, you can rearrange that equation to solve for the missing one.
How do you solve for an unknown using cross multiplication?
Cross multiply to turn a/b = c/d into a × d = b × c, then divide both sides by the term next to the unknown to isolate it. For example, solving for d gives d = (b × c) ÷ a.
Why do the two cross products have to be equal?
In a true proportion, a/b and c/d represent the same ratio. Multiplying both sides of a/b = c/d by b×d clears the denominators and leaves a × d = b × c, so if the proportion is valid, those two products must match exactly.
What happens if one of the known terms is zero?
Solving requires dividing by the term next to the unknown, so that term can't be zero. For example, d = (b × c) ÷ a is undefined if a = 0, since division by zero has no answer.

Related calculators