How to solve a proportion
A proportion states that two ratios are equal: a/b = c/x. To find the missing value x, cross multiply: a × x = b × c, so x = b × c ÷ a. With a = 2, b = 3 and c = 8, x = 3 × 8 ÷ 2 = 12.
Cross multiplication is not a trick but a shortcut for multiplying both sides by b and by x at once, which clears both denominators in a single step. A quick sanity check confirms the result: 2/3 and 8/12 both reduce to the same ratio, so the two fractions really are equal. A proportion is two ratios set equal, so it helps to tidy both sides with the ratio calculator first.
Where proportions are used
Proportions scale recipes, convert units, resize images and solve similar-triangle problems. Any time two quantities keep a constant ratio, a proportion finds the unknown. For comparing two values as a percentage, see the percent difference calculator.
How to use this calculator
Enter the three known values a, b and c — the calculator solves for x in a/b = c/x. The value of a must not be zero, since division by zero is undefined. The result updates instantly. Scaling a part against a whole of 100 is the same move made by the percentage calculator.
- Keep the pairing consistent. If a and c are both in the same unit, b and x must be in the other unit throughout.
- Watch the position of a. It is the denominator in the solution, so swapping it with c changes the answer.
- Decimals and negatives are both accepted.
Frequently asked questions
- How do I solve a/b = c/x?
- Cross multiply and rearrange: x = b × c ÷ a. For 2/3 = 8/x, x = 3 × 8 ÷ 2 = 12.
- What is cross multiplication?
- Cross multiplication multiplies each numerator by the opposite denominator, turning a/b = c/x into a × x = b × c.
- Why can't a be zero?
- Solving for x divides by a, and division by zero is undefined, so a must be non-zero.
- Can I use decimals?
- Yes. The calculator accepts decimal values for a, b and c.
- What if the unknown sits in a different position?
- Relabel the proportion so the unknown lands in the x slot. Since a/b = c/x can be flipped to b/a = x/c or rewritten as a/c = b/x, any of the four positions can be moved into place before entering your three known numbers.