How to use the proportion calculator
A proportion is a statement that two ratios are equal: a/b = c/d. Type the three numbers you know and leave the fourth box empty (an empty box and a 0 are treated the same). The calculator solves for the unknown by cross-multiplication and shows the step. If you fill in all four boxes, it checks the cross products and tells you whether the proportion is true.
Cross-multiplication
Multiply both sides of a/b = c/d by b × d and the fractions disappear: a × d = b × c. The products of the diagonals are equal — that is the whole trick. Whichever term is missing, multiply the two terms on the other diagonal and divide by the one that is left:
| Unknown | Formula | Example |
|---|---|---|
| a | a = b × c ÷ d | a/5 = 8/10 → a = 5 × 8 ÷ 10 = 4 |
| b | b = a × d ÷ c | 2/b = 6/9 → b = 2 × 9 ÷ 6 = 3 |
| c | c = a × d ÷ b | 2/12 = c/30 → c = 2 × 30 ÷ 12 = 5 |
| d | d = b × c ÷ a | 3/4 = 9/d → d = 4 × 9 ÷ 3 = 12 |
Worked example
Solve 3/4 = 9/d. Cross-multiply: 3 × d = 4 × 9 = 36. Divide both sides by 3: d = 36 ÷ 3 = 12. Check it by turning both ratios into decimals: 3 ÷ 4 = 0.75 and 9 ÷ 12 = 0.75. They match, so the proportion holds.
Direct and inverse proportion
Two quantities are in direct proportion when they grow together at a fixed rate: y = k × x. Double the amount of fabric and the cost doubles; drive twice as long at the same speed and you cover twice the distance.
They are in inverse proportion when one grows as the other shrinks and their product stays fixed: x × y = k. More painters, less time; higher speed, shorter trip. To solve an inverse problem with this tool, flip one of the ratios so that the product rule a × d = b × c matches. If 4 painters finish a job in 6 hours, 6 painters take: 4/6 = t/6, so 4 × 6 = 6 × t and t = 4 hours. Check: 4 painters × 6 hours = 24 painter-hours = 6 painters × 4 hours.
Everyday proportion problems
- Map scale: on a 1 : 50,000 map, two villages are 3.4 cm apart. 1/50,000 = 3.4/d → d = 170,000 cm = 1.7 km.
- Recipe scaling: 2 cups of flour make 12 cookies. For 30 cookies: 2/12 = c/30 → c = 5 cups.
- Currency: at a rate where $100 buys €92, $350 buys 100/92 = 350/d → d = €322. (Use the rate your bank quotes that day.)
- Unit price: 3 lb of apples cost $4.47; 5 lb cost 3/4.47 = 5/d → d = $7.45.
- Percent: part/whole = percent/100, so 45 out of 60 is 45/60 = p/100 → p = 75%. The percentage calculator has shortcuts for these.
Checking whether a proportion is true
Is 2/3 = 4/6? The cross products are 2 × 6 = 12 and 3 × 4 = 12 — equal, so yes. Is 2/3 = 5/7? 2 × 7 = 14 and 3 × 5 = 15 — not equal, so no, although the decimals 0.667 and 0.714 are close. Testing a proportion is the same as asking whether two ratios are equivalent; the ratio calculator does that too and simplifies both ratios for you.
Frequently asked questions
What is cross-multiplication?
For a proportion a/b = c/d, multiplying the numerator of each fraction by the denominator of the other gives a × d = b × c. It works because both sides of the equation were multiplied by b × d, which clears the fractions without changing the solution.
Can I use decimals or negative numbers?
Yes, any real numbers work — 1.5/2.5 = c/10 gives c = 6. The only restriction is that the term you divide by cannot be zero, which is why a 0 is read as the empty, unknown box.
Why does the calculator treat 0 as the unknown?
An empty box and a 0 are the same to the tool. A proportion with a zero term would force another term to be zero as well, which has no single useful solution, so 0 is reserved for marking the box you want solved.
What is the difference between a ratio and a proportion?
A ratio compares two numbers (3 : 4). A proportion is an equation saying two ratios are equal (3 : 4 = 9 : 12). You simplify a ratio; you solve a proportion.
How do I solve an inverse proportion problem?
Flip one of the two ratios before cross-multiplying, so the equation becomes x₁ × y₁ = x₂ × y₂. For 4 painters taking 6 hours, 6 painters take 4/6 = t/6, giving t = 4 hours.
Last updated: October 9, 2026