This proportion calculator solves a proportion — two equal ratios — for whichever value is missing. Leave one box empty, fill the other three, and get the answer with the cross-multiplication laid out.
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How Proportions Work
A proportion states that two ratios are the same relationship at different scales: 3/4 = 15/20. The solving engine is cross-multiplication: in a/b = c/d, always a×d = b×c, so any single unknown falls out by division. Proportions are how recipes scale, maps convert, models relate to prototypes and similar triangles resolve — the practical partner of our Ratio Calculator (which simplifies and splits ratios). Part of our Math Calculators collection.
Worked Examples (Verified)
- 3/4 = x/20: cross-multiply: 4x = 60 → x = 15
- 5/x = 15/9: 15x = 45 → x = 3 (sanity: 5/3 and 15/9 both simplify to 5/3 ✔)
- Real life: a recipe for 4 uses 3 cups of flour; for 20 people (5× the batch): 3/4 = x/20 → 15 cups — the first example wearing an apron
Direct vs. Inverse Proportions (Do Not Mix Them)
- Direct: both sides grow together (ingredients ↔ servings). Solved by the calculator above.
- Inverse: one grows as the other shrinks (workers ↔ days to finish). These follow a×b = constant instead — 4 workers × 6 days = 24 worker-days, so 8 workers take 3 days. Setting an inverse problem into a direct proportion is the classic classroom trap.
- Unit-rate check: reduce one side to “per 1” (3/4 = 0.75 per unit) and multiply — an excellent sanity check on any proportion answer.
Related Tools
- Ratio Calculator — simplify and split ratios
- Math Calculators — the full collection
Frequently Asked Questions
How do I solve a proportion?
Cross-multiply and divide: for a/b = c/x, x = b×c ÷ a. The calculator performs it for whichever position is unknown.
What is cross-multiplication?
The rule that a/b = c/d implies a×d = b×c — multiply each numerator by the opposite denominator. It is just both fractions scaled to a common denominator, compressed.
How do I check a proportion answer?
Simplify both ratios — they must reduce to the same fraction (5/x = 15/9 with x = 3: 5/3 and 5/3 ✔). Or use the unit rate as described above.
What is the difference between a ratio and a proportion?
A ratio is one comparison (3:4); a proportion is an equation claiming two ratios are equal (3:4 = 15:20). This calculator solves the equation kind.
Can proportions have decimals or fractions inside?
Yes — cross-multiplication is pure algebra and handles any real numbers, which is why the calculator accepts decimals in every box.
Is this proportion calculator free?
Yes — free, instant, no sign-up.