Cross Multiplication Calculator
Enter any three values in the proportion A/B = C/D and this calculator finds the fourth using cross multiplication. Choose which variable to solve for, fill in the other three, and the answer appears instantly with every step of the working. Handles whole numbers, decimals, and negative values.
Formula
Worked example
Given A = 3, B = 4, C = 6, solve for D. Cross multiply: 3 x D = 4 x 6 = 24. Divide both sides by 3: D = 8. Verify: 3/4 = 0.75 and 6/8 = 0.75. Correct.
What is cross multiplication?
Cross multiplication is the algebraic step that clears fractions from a proportion. When you have A/B = C/D, multiplying both sides by the product of the two denominators (B x D) gives A x D = B x C. The "cross" in the name comes from the diagonal pattern: A (top-left) is paired with D (bottom-right) while B (bottom-left) is paired with C (top-right). This identity is the foundation for solving proportions in arithmetic, algebra, chemistry, cooking, map reading, and a wide range of everyday calculations.
How to use this calculator
Select which variable you want to find from the "Solve for" dropdown, then enter the three known values. The calculator resolves the proportion instantly and displays the full working: it writes the equation, applies cross multiplication, computes both cross-products, isolates the unknown, and verifies the result. All four solve modes are supported (A, B, C, or D). You can use whole numbers, decimals, or negative values. The only restriction is that a known denominator (B when solving for anything other than B, or D when solving for anything other than D) cannot be zero.
Worked example: scaling a recipe
A recipe for 4 servings uses 3 cups of flour. How much flour is needed for 10 servings? Set up the proportion: 3/4 = x/10. Cross multiply: 3 x 10 = 4 x x, so 30 = 4x, giving x = 7.5 cups. In this calculator, enter A = 3, B = 4, D = 10 and choose "Solve for C" to get C = 7.5. The same approach handles currency exchange, dilution ratios, speed conversions, and blueprint scaling.
Comparing fractions with cross multiplication
Cross multiplication also settles which of two fractions is larger without finding a common denominator. For A/B and C/D (with positive denominators), compute A x D and B x C. If A x D is greater, then A/B is larger. If B x C is greater, then C/D is larger. Equal products mean the fractions are equivalent. Example: comparing 3/7 and 5/11 gives 3 x 11 = 33 and 7 x 5 = 35. Since 35 > 33, we conclude 5/11 > 3/7.
Real-world uses of proportions
Proportions appear in almost every practical context. In cooking, you scale ingredient quantities. In maps, you convert scale distances to real distances. In chemistry, you use unit factors to change between milligrams, grams, and moles. In finance, you calculate currency exchange: if 1 USD = 0.93 EUR, how many EUR do you get for 250 USD? Set up 1/0.93 = 250/x. In construction, you translate blueprint dimensions to actual measurements. In medicine, a pharmacist uses proportions to calculate dosage: if 500 mg is contained in 2 mL, how many mL hold 750 mg?
Cross multiplication formulas for each unknown
| Solve for | Formula | Requires |
|---|---|---|
| A | A = (B x C) / D | D not zero |
| B | B = (A x D) / C | C not zero |
| C | C = (A x D) / B | B not zero |
| D | D = (B x C) / A | A not zero |
In A/B = C/D, cross multiplication gives A x D = B x C. Rearranging yields a direct formula for each variable.
Frequently asked questions
What does cross multiplication mean?
Cross multiplication converts the proportion A/B = C/D into the simpler equation A x D = B x C by multiplying both sides by B x D to remove the denominators. The term "cross" refers to the diagonal pattern: A pairs with D across one diagonal, and B pairs with C across the other.
How do I solve 3/4 = x/8?
Cross multiply: 3 x 8 = 4 x x, giving 24 = 4x. Divide both sides by 4 to get x = 6. Verify: 3/4 = 0.75 and 6/8 = 0.75, confirming the answer.
Can I use decimals or negative numbers?
Yes. The calculator handles any real number: decimals, negatives, and fractions entered as decimals (for example 0.5 for 1/2). The only restriction is that a known denominator cannot be zero, because division by zero is undefined.
Why does cross multiplication work?
It is a shortcut for multiplying both sides by the same quantity. Starting from A/B = C/D, multiplying both sides by B x D gives (A x B x D) / B = (C x B x D) / D, which simplifies to A x D = B x C. The operation is valid as long as B and D are both non-zero.
How do I use cross multiplication to compare fractions?
For fractions A/B and C/D with positive denominators, compute A x D and B x C. If A x D is larger, then A/B is the bigger fraction. If B x C is larger, then C/D is bigger. If both products are equal, the fractions have the same value. This avoids the need to find a common denominator.
What is the difference between a proportion and a ratio?
A ratio compares two quantities, for example 3:4 or 3/4. A proportion states that two ratios are equal, for example 3/4 = 6/8. Cross multiplication is used to solve or verify proportions, not standalone ratios.
Can cross multiplication find a denominator?
Yes. If you need B or D (a denominator), select the appropriate option from the "Solve for" menu. For A/B = C/D, solving for B gives B = (A x D) / C, and solving for D gives D = (B x C) / A. Both are handled automatically.