A proportion says that two fractions (or ratios) are equal: a/b = c/d. When one of the four numbers is unknown, cross-multiplication finds it. Proportions are behind scaling recipes, map distances, unit prices, similar triangles and dosage calculations. This calculator lets you put the unknown in any position and solves exactly.
How to use the proportion solver
- The four boxes are arranged like the proportion: A over B on the left, C over D on the right.
- Type x in the box you want to find and numbers in the other three. Fractions (1/2), mixed numbers (1 1/2) and decimals are accepted.
- The tape shows x as a fraction, as a mixed number if it is larger than 1, and as a decimal, plus the value both ratios share. The proportion is redrawn with x filled in.
Cross-multiplication
Multiplying both sides of the proportion by b × d cancels both denominators, leaving the two diagonal products equal. Then:
| Unknown | Solve with |
|---|---|
| a | a = b × c ÷ d |
| b | b = a × d ÷ c |
| c | c = a × d ÷ b |
| d | d = b × c ÷ a |
Worked example: 3/4 = x/20
- Cross-multiply: 3 × 20 = 4 × x, so 60 = 4x.
- Divide both sides by 4: x = 15.
- Check: 3/4 = 0.75 and 15/20 = 0.75. ✓
A fractional example: (1/2)/3 = x/(1 1/2). Cross-multiplying gives (1/2) × (3/2) = 3x, so 3/4 = 3x and x = 1/4. Both ratios equal 1/6.
Setting up word problems
Write each ratio with the same kind of quantity in the same position.
Recipe: 3 cups of flour make 24 cookies. How much flour for 40 cookies? 3/24 = x/40, so x = 3 × 40 ÷ 24 = 5 cups.
Map scale: 1 inch = 15 miles. How many inches for 85 miles? 1/15 = x/85, so x = 85 ÷ 15 = 5 2/3 inches.
The key is consistency: if the first ratio is flour over cookies, the second must be flour over cookies too.
Things to watch
- Zero denominators are never allowed, so B and D cannot be 0.
- Only one unknown. With two unknowns there are infinitely many solutions.
- Not every pair of ratios is a proportion. If you fill in all four numbers, check whether the cross products match — that is how the equivalent fractions calculator tests equality.
For ratios written with colons (A:B = C:D) and scaling ratios up or down, see the ratio calculator; for prices and speeds, the unit rate calculator finds the amount per one unit.
Frequently asked questions
How do you solve for x in a proportion?
Cross-multiply and divide. In a/b = c/d, the cross products are equal: a × d = b × c. Put x in its place, multiply the two known diagonal numbers, and divide by the number next to x. For 3/4 = x/20: 3 × 20 = 4x, so x = 60 ÷ 4 = 15.
Can x be in the denominator?
Yes. Type x in any of the four boxes. For 3/x = 6/10, cross-multiplying gives 3 × 10 = 6x, so x = 30 ÷ 6 = 5.
Can the known values be fractions or decimals?
Yes. Each box accepts whole numbers, decimals, fractions such as 1/2 and mixed numbers such as 1 1/2. The answer is given as an exact fraction and as a decimal.
When does a proportion have no solution?
If x would have to be 0 in a denominator, or if the number multiplying x is 0 while the other side is not, there is no solution. For example 0/x = 5/7 has no solution, since 0 divided by anything is 0, not 5/7.