Proportion Calculator

1. Pick the missing value

Choose A, B, C, or D — whichever number you don't know. Its input box is disabled so you can't accidentally type into it.

2. Enter the three known values

Type the numbers you do know. Decimals and negative numbers are fine. The two denominators (B and D) cannot be zero.

3. Read the answer and the steps

The result appears instantly as you type, or press Calculate. Below the answer you'll see each cross-multiplication step with your own numbers, plus a check that both sides are equal.

Step 1. Write the proportion: 3/5 = x/15.
Step 2. Cross multiply: 5 × x = 3 × 15.
Step 3. Simplify: 5x = 45.
Step 4. Divide both sides by 5: x = 45 ÷ 5.
Step 5. x = 9. Check: 3 ÷ 5 = 0.6 and 9 ÷ 15 = 0.6 ✓

Step 1. Write the proportion: x/4 = 6/8.
Step 2. Cross multiply: 8 × x = 4 × 6.
Step 3. Simplify: 8x = 24.
Step 4. Divide both sides by 8: x = 24 ÷ 8.
Step 5. x = 3. Check: 3 ÷ 4 = 0.75 and 6 ÷ 8 = 0.75 ✓

Step 1. Write the proportion: 2/7 = 6/x.
Step 2. Cross multiply: 2 × x = 7 × 6.
Step 3. Simplify: 2x = 42.
Step 4. Divide both sides by 2: x = 42 ÷ 2.
Step 5. x = 21. Check: 2 ÷ 7 ≈ 0.2857 and 6 ÷ 21 ≈ 0.2857 ✓

A proportion is an equation that says two ratios are equal. If 1/2 and 2/4 describe the same relationship, we write 1/2 = 2/4 and call it a proportion. The two ratios are called equivalent ratios — they may look different, but they reduce to the same value.

Proportions show up anywhere a relationship has to stay constant while the numbers scale: doubling a recipe, converting currencies, reading a map, or mixing a solution to the right strength. Solving a proportion means finding the one number that keeps both sides equal.

A ratio compares two quantities — for example, a class with 3 girls for every 5 boys has a girl-to-boy ratio of 3/5. It is a single comparison, not an equation.

A proportion goes one step further: it states that two ratios are equal, like 3/5 = 9/15. If the class grows but keeps the same mix, 9 girls to 15 boys preserves the ratio — and the proportion is the equation that says so.

Memory aid: a ratio is a comparison; a proportion is an equation about two comparisons.

Direct proportion

Both quantities move in the same direction: double one, the other doubles. Pay for hours worked is a classic example — 2 hours earns $36, so 5 hours earns x: set up 2/36 = 5/x and solve to get x = 90. The calculator above handles this directly once the two ratios are identified.

Inverse proportion

One quantity goes up while the other goes down: their product stays constant. If 4 workers finish a job in 6 days, 8 workers take x days — 4 × 6 = 8 × x, so x = 3. Note the setup differs (equal products, not equal ratios), so arrange an inverse problem into the a/b = c/d form before using the calculator.

Scaling a recipe

A recipe uses 2 cups of flour for 12 cookies. For 30 cookies: 2/12 = x/30 → x = 5 cups. Every scaling problem is a proportion in disguise.

Map scales

On a 1:50,000 map, 1 cm represents 50,000 cm (0.5 km) in the real world. Measure the map distance, set up the proportion, and solve for the real distance.

Unit conversion and mixing

Currency exchange, medicine dosing by weight, and paint or concrete mixing ratios all keep one relationship constant while the quantities change — exactly what a/b = c/d describes.

Flipping one ratio

Writing a/b = d/c instead of a/b = c/d. Keep the same order on both sides: numerators with numerators, denominators with denominators.

Adding instead of cross multiplying

Proportions are solved by multiplication, not addition. If the "difference" between 3 and 5 tempts you, remember: ratios scale by multiplication.

Zero denominators

A ratio with a zero denominator is undefined, so any proportion containing one has no meaning. This calculator refuses zero denominators rather than showing a misleading answer.

Rounding too early

Round only the final answer. Rounding intermediate steps (like a repeating decimal) carries the error into the result.

This calculator performs exact arithmetic on the numbers you enter — it cannot check whether those numbers correctly describe your real-world situation. Setting up the proportion (deciding which quantities form the two ratios, and in which order) is the part that requires judgment; the worked examples above show how to do it. Results are displayed rounded to 6 decimal places; the underlying calculation keeps full precision. A missing denominator that would have to be zero has no valid solution, and the calculator says so instead of guessing.