Proportion Solver
Quick answer: A proportion a/b = c/d solves by cross-multiplication: multiply diagonally to get a×d = b×c, then divide to isolate the unknown. For example, 3/4 = x/20 gives 4x = 3 × 20 = 60, so x = 15. Fill in any three values below and the solver finds the fourth, showing every step.
This proportion solver finds the missing value in any direct proportion a/b = c/d. Enter any three of the four values — leave the unknown blank — and get the answer instantly with the cross-multiplication steps shown.
Enter three values
a/b = c/d — leave exactly one field blank.
Your results
| Proportion solved | — |
How to use this calculator
Type three known values into the four fields and leave the unknown one blank. The solver runs as you type, and the button recalculates on demand. Denominators b and d cannot be zero.
If the answer is not what you expected, double-check that the proportion is set up the right way round — matching quantities must sit in the same position on both sides (for example, cups of flour on the top of both fractions).
How it works
Cross-multiplication: a/b = c/d is equivalent to a × d = b × c, because multiplying both sides by b×d clears the denominators. To isolate the unknown, divide both sides by the number multiplying it: a = b×c/d, b = a×d/c, c = a×d/b, d = b×c/a. The solver requires exactly one blank field and non-zero denominators; it only solves direct proportions.
Worked example
Solve 3/4 = x/20. Cross-multiply: 4 × x = 3 × 20, so 4x = 60. Divide both sides by 4: x = 60 ÷ 4 = 15. Check: 3 ÷ 4 = 0.75 and 15 ÷ 20 = 0.75.
Reference data
| Proportion | Cross-multiplied form | Solve for each unknown |
|---|---|---|
| a/b = c/d | a × d = b × c | a = b×c/d; b = a×d/c; c = a×d/b; d = b×c/a |
Source: derived from the standard cross-multiplication rule of arithmetic; no external 2026 data table applies to this tool.
Method & sources
Formula: from a/b = c/d, cross-multiply to a×d = b×c, then divide to isolate the unknown. Edge cases: exactly one of a, b, c, d must be blank; b and d must be non-zero (they are denominators); the divisor for the specific unknown must also be non-zero.
- The cross-multiplication rule is derived from elementary arithmetic; it is not sourced from an external publication.
- This tool solves direct proportions only (a/b = c/d), not inverse proportions.
Frequently asked questions
What is a proportion?
A proportion is an equation stating that two ratios are equal, written a/b = c/d. It says the fraction a over b has the same value as the fraction c over d.
How does cross-multiplication work?
Multiply the numerator of one side by the denominator of the other: a/b = c/d becomes a × d = b × c. This works because multiplying both sides of the equation by bd clears the denominators. Then divide to isolate the unknown.
Does this solver handle inverse proportions?
No. This tool solves direct proportions of the form a/b = c/d. Inverse proportions (where one quantity rises as the other falls, like a × b = k) need a different setup and are not covered here.