✖️ Cross Multiplication Calculator
By ToolNimba Math Team · Updated 2026-06-19
Enter a proportion in the form a/b = c/d and leave exactly ONE box blank (type x or just clear it). The calculator cross multiplies to solve for the missing value.
Cross multiplication is the quickest way to solve a proportion: two ratios set equal, a/b = c/d. When one of the four values is unknown, you cross multiply to turn the equation into a simple line you can solve in one step. Type three of the four values, leave the fourth box blank (or write x), and this calculator finds the missing value and shows the cross-multiply working so you can check it by hand.
What is the Cross Multiplication Calculator?
A proportion is a statement that two ratios are equal, written a/b = c/d. Cross multiplication uses one fact: if two fractions are equal, then the product of the diagonals is equal too. Multiplying a/b = c/d by both denominators clears the fractions and leaves a x d = b x c. The two diagonal products (a with d, and b with c) are called the cross products, and in any true proportion they always match.
Once the fractions are gone, solving for the unknown is straightforward division. If x sits in the d position of a/b = c/x, cross multiplying gives a x x = b x c, so x = (b x c) / a. The pattern is the same wherever the unknown sits: build the two cross products, then divide the product that does not contain the unknown by the number that multiplies it. The calculator does this automatically and labels each step.
One value is off limits as a divisor: zero. Because solving always ends in a division, if the number you must divide by is 0, the proportion has no finite solution. That happens, for example, when the numerator on the same side as the unknown is paired with a zero across the diagonal. The calculator detects this and tells you rather than returning a meaningless answer.
When to use it
- Finding a missing term in a math proportion when three of the four values are known.
- Scaling a recipe, map distance or model: if 2 cups serve 3 people, how many cups serve 8?
- Converting between units or currencies where a known rate sets the ratio.
- Checking similar triangles or scale drawings, where corresponding sides stay in proportion.
- Working out percentages, mixtures and dosages that are expressed as part-to-whole ratios.
How to use the Cross Multiplication Calculator
- Enter the three values you know into boxes a, b, c and d (the layout is a/b = c/d).
- Leave exactly one box blank, or type x in it, to mark the value you want to solve for.
- Press Solve (or just edit a box) to cross multiply and read the missing value.
- Check the two working lines: the cross-multiply step and the division that gives the answer.
- Use Reset to return to the worked sample proportion at any time.
Formula & method
Worked examples
Solve the proportion 2/3 = 8/x for the missing value x.
- Write the proportion: 2/3 = 8/x
- Cross multiply (diagonal products are equal): 2 x x = 3 x 8
- That gives 2x = 24
- Divide both sides by 2: x = 24 / 2
- x = 12, so 2/3 = 8/12 (and 8/12 reduces back to 2/3, confirming it)
Result: x = 12
A recipe uses 4 eggs for 6 servings. How many eggs (x) are needed for 15 servings?
- Set up the proportion eggs/servings: 4/6 = x/15
- Cross multiply: 4 x 15 = 6 x x
- That gives 60 = 6x
- Divide both sides by 6: x = 60 / 6
- x = 10 eggs for 15 servings
Result: x = 10 eggs
Solve x/5 = 9/15, where the unknown is in the numerator on the left.
- Write the proportion: x/5 = 9/15
- Cross multiply: x x 15 = 5 x 9
- That gives 15x = 45
- Divide both sides by 15: x = 45 / 15
- x = 3
Result: x = 3
Where the unknown sits and the formula used to solve it (proportion a/b = c/d)
| Unknown position | Cross-multiply equation | Solve with | Divisor must not be |
|---|---|---|---|
| a (top left) | a x d = b x c | a = (b x c) / d | d = 0 |
| b (bottom left) | a x d = b x c | b = (a x d) / c | c = 0 |
| c (top right) | a x d = b x c | c = (a x d) / b | b = 0 |
| d (bottom right) | a x d = b x c | d = (b x c) / a | a = 0 |
Quick sample proportions and their solutions
| Proportion | Cross products | Missing value |
|---|---|---|
| 2/3 = 8/x | 2x = 24 | x = 12 |
| x/5 = 9/15 | 15x = 45 | x = 3 |
| 7/x = 21/9 | 63 = 21x | x = 3 |
| x/4 = 2.5/10 | 10x = 10 | x = 1 |
Common mistakes to avoid
- Multiplying straight across instead of diagonally. Cross multiplication pairs each numerator with the OTHER fraction denominator (the diagonals). Multiplying a with b, or c with d, on the same side is wrong and gives a meaningless equation.
- Dividing by the wrong number. After cross multiplying, divide the product that does NOT contain the unknown by the number that multiplies the unknown. For 2x = 24 you divide 24 by 2, not 2 by 24.
- Setting up the ratio inconsistently. Both ratios must compare the same things in the same order, for example eggs over servings on both sides. Flipping one fraction (servings over eggs) gives the wrong answer.
- Ignoring a zero divisor. If solving forces you to divide by zero, the proportion has no finite solution. A result of "no solution" is information, not a calculator error.
Glossary
- Ratio
- A comparison of two quantities by division, such as a to b, written a/b or a:b.
- Proportion
- A statement that two ratios are equal, written a/b = c/d.
- Cross product
- A diagonal product in a proportion: a times d, or b times c. In a true proportion the two cross products are equal.
- Cross multiplication
- The method of multiplying the diagonals of a proportion to clear the fractions and solve for an unknown.
- Numerator
- The top number of a fraction or ratio.
- Denominator
- The bottom number of a fraction or ratio; it must not be zero.
Frequently asked questions
What is cross multiplication?
Cross multiplication is a method for solving a proportion a/b = c/d. You multiply the diagonals to get a x d = b x c, which clears the fractions. Because the two ratios are equal, their cross products are equal too, leaving a simple equation you can solve by dividing.
How do I solve for x in a/b = c/x?
Cross multiply to get a x x = b x c, which is a x = b c. Then divide both sides by a, so x = (b x c) / a. For example, 2/3 = 8/x becomes 2x = 24, and dividing by 2 gives x = 12.
Which box should I leave blank?
Leave blank the single value you want to find, in whichever of the four positions it belongs (a, b, c or d). Type the other three as numbers. You can clear the box or type x to mark it as the unknown. Exactly one box must be blank.
Why does the calculator say there is no solution?
Solving a proportion always ends in a division. If the number you would have to divide by is zero, there is no finite answer, so the tool reports no solution instead of an error. This usually means the inputs do not form a valid proportion.
Can I use decimals and negative numbers?
Yes. Any of the three known values can be a decimal or a negative number, and the cross-multiply steps work the same way. The only restriction is that you cannot end up dividing by zero when solving for the unknown.
Does cross multiplication work for any proportion?
It works for any equation of two equal ratios, a/b = c/d, with one unknown. It does not solve equations with two or more unknowns, or expressions that are not a single ratio equal to another single ratio. For those you need other algebra methods.