Cross Multiplication Calculator
Solve an equation of the form a/b = c/x by cross-multiplying. Enter a, b and c to get x, with the cross product and each line of working shown so you can follow or copy the method.
- Cross product (b × c)
- 160
- Working
- 5 × x = 8 × 20 = 160, so x = 160 ÷ 5 = 32
Saved setups
Save a set of inputs you reuse — your usual rate, your loan, your room sizes — and load it back in one tap.
Your recent calculations
Results you calculate here are kept on this device so you can come back to them.
Formula
How to use it
- Write your problem so the unknown is the bottom-right number.
- Enter a (top left), b (bottom left) and c (top right).
- Read x and follow the working line to see how it was found.
Worked examples
5/8 = 20/x
- x (bottom right)
- 32
- Cross product (b × c)
- 160
- Working
- 5 × x = 8 × 20 = 160, so x = 160 ÷ 5 = 32
3/7 = 12/x
- x (bottom right)
- 28
- Cross product (b × c)
- 84
Why cross-multiplying works
Multiplying both sides of a/b = c/x by b × x clears both denominators at once and leaves a × x = b × c. It is a shortcut for two ordinary steps, not a separate rule.
It only applies across an equals sign between two fractions. It is not a way to add or multiply fractions.
Comparing fractions with cross products
To see which of 5/8 and 7/12 is larger, cross-multiply: 5 × 12 = 60 and 8 × 7 = 56. The first product is bigger, so 5/8 is the larger fraction.
Questions people ask
How do I solve 5/8 = 20/x?
Cross-multiply to get 5 × x = 8 × 20 = 160, then divide by 5: x = 32.
How do I solve 3/7 = 12/x?
3 × x = 7 × 12 = 84, so x = 28.
What if the unknown is in a different position?
Flip both fractions or swap the sides so the unknown lands bottom right — the equation stays true — or use the proportion calculator, which solves for any of the four terms.