What this calculator does
Cross-multiplying is the standard way to solve a proportion, a statement that two ratios are equal, when one of the four numbers is unknown. Given a/b = c/d, cross-multiplying turns it into a×d = b×c, a plain equation with no fractions left in it, which can then be rearranged to isolate whichever value is missing.
This calculator does exactly that: enter the three known values in a proportion, mark which one is unknown, and it cross multiplies to solve for it. The same method covers recipe scaling, map distances, unit price comparisons and any other "if this, then that" ratio problem.
The formula
Cross-multiplication rewrites a/b = c/d as a×d = b×c by multiplying each numerator by the opposite denominator. Whichever of a, b, c or d is unknown is then isolated by dividing both sides by the other value on its side of the equation.
| Term | Meaning |
|---|---|
| a, b, c, d | The four values in the proportion a/b = c/d. Any one of them can be the unknown. |
| Proportion | A statement that two ratios are equal, such as 3/4 = 9/12. |
| Cross-multiply | Multiplying a numerator by the denominator diagonally across from it: a×d and b×c. |
The inputs explained
| Field | What to enter |
|---|---|
| a (leave as 0 if this is the unknown) | The first numerator. If a is the unknown, leave this at 0 and select "a" below. |
| b | The first denominator. |
| c | The second numerator. |
| d (leave as 0 if this is the unknown) | The second denominator. If d is the unknown, leave this at 0 and select "d" below. |
| Which value is unknown | Which of the four values you want to solve for. |
When to use it
Scaling a recipe
A recipe that serves 4 needs 3 cups of flour; how many cups for 10 servings? Set up 3/4 = c/10 and cross multiply to find c.
Converting a map distance
A map scale of 1 cm to 20 km, and a measured distance of 7.5 cm: cross-multiplying 1/20 = 7.5/d finds the real-world distance d.
Checking if two ratios are equivalent
Solving for the missing side of a proportion and comparing it against a known value confirms whether two ratios, such as two mixing strengths, are actually equal.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
Solving 3/4 = 9/d for different values of 9
Holding a=3 and b=4 fixed, and varying c, shows how the solved value of d changes.
Questions
What is cross-multiplication used for?
It solves a proportion, an equation of the form a/b = c/d, for any one unknown value by clearing the fractions: multiply each numerator by the denominator diagonally opposite it, giving a×d = b×c.
How to cross multiply fractions step by step?
Write the two fractions as equal, a/b = c/d. Multiply a by d and b by c to get a×d = b×c. Then divide both sides by whichever term sits next to the unknown to isolate it.
Does cross-multiplication work for any two fractions?
It works for solving a proportion, where the two fractions are stated to be equal. It is not a general way to add or compare unrelated fractions; for that, a common denominator is the right tool.
What if the denominator I am solving for turns out to be zero?
That means the known values you entered cannot form a valid proportion with a finite answer. Double-check the values, since a genuine proportion problem will not require dividing by zero.
For plain fraction-to-percentage conversions rather than solving a proportion, see the percentage calculator.