⚖️ Proportion Calculator (Solve for X)
By ToolNimba Team · Updated 2026-06-19
Enter three values and leave exactly one box blank. The blank box is solved using cross multiplication (A times D equals B times C).
A proportion says that two ratios are equal, written as A divided by B equals C divided by D. This calculator solves a proportion for any one unknown when you know the other three values. Type three numbers, leave a single box blank, and press Solve. The tool cross multiplies and shows the exact step it used to reach the answer.
Proportions show up everywhere: scaling a recipe, converting map distances, mixing paint, sizing photos, working out unit prices, and answering school problems that ask you to solve for x. Because the math runs entirely in your browser, nothing you enter is sent anywhere.
What is the Proportion Calculator?
Two ratios are in proportion when they describe the same relationship at a different scale. If A divided by B equals C divided by D, then the pair A and B keeps the same balance as the pair C and D. The classic way to solve such an equation is cross multiplication: multiply each numerator by the opposite denominator so that A times D equals B times C. That single rule lets you isolate whichever value is missing.
Once you have A times D equals B times C, basic algebra finishes the job. To find the missing top value, multiply the two known numbers that sit diagonally and divide by the remaining known number. For example, to solve for A you compute B times C, then divide by D. The same idea works for B, C, or D by rearranging the equation so the unknown stands alone on one side.
The only situation that has no answer is when solving would require dividing by zero. That happens when the value sitting in the denominator of your rearranged equation is zero. In every other case there is exactly one solution, which this calculator reports along with the worked step so you can check it by hand.
When to use it
- Solving for x in a school or homework proportion such as 3/4 = x/20.
- Scaling a recipe up or down while keeping ingredient ratios the same.
- Converting map distance to real distance using a scale ratio.
- Finding a missing dimension when resizing an image at a fixed aspect ratio.
- Working out unit price or best value when comparing different pack sizes.
- Mixing paint, fuel, or chemicals to a required ratio.
How to use the Proportion Calculator
- Enter three of the four values into the boxes labelled A, B, C, and D.
- Leave exactly one box blank: that blank is the value you want to find.
- Press the Solve button (or hit Enter inside any box).
- Read the missing value in the highlighted result panel.
- Check the worked line below it to see the cross-multiplication step used.
- Use Clear all to reset every box and start a new proportion.
Formula & method
Solve A = (B × C) ÷ D
Solve B = (A × D) ÷ C
Solve C = (A × D) ÷ B
Solve D = (B × C) ÷ A
Worked examples
Solve 3/4 = x/20 for the missing top-right value.
- Identify the values: A = 3, B = 4, C = x (blank), D = 20.
- Cross multiply: A times D = B times C, so 3 times 20 = 4 times x.
- That gives 60 = 4x.
- Divide both sides by 4: x = 60 divided by 4.
Result: x = 15
Solve 2/5 = 8/x for the missing bottom-right value.
- Identify the values: A = 2, B = 5, C = 8, D = x (blank).
- To find D, compute B times C divided by A.
- B times C = 5 times 8 = 40.
- Divide by A: 40 divided by 2 = 20.
Result: x = 20
A recipe for 4 servings needs 6 eggs. How many eggs for 10 servings? Solve 4/6 = 10/x.
- Set servings over eggs: 4/6 = 10/x, so A = 4, B = 6, C = 10, D = x.
- Find D using B times C divided by A.
- B times C = 6 times 10 = 60.
- Divide by A: 60 divided by 4 = 15.
Result: x = 15 eggs
Which value you are solving for and the formula the calculator applies
| Missing value | Formula used | Plain-language version |
|---|---|---|
| A (top left) | A = (B times C) / D | Multiply the two known diagonals, divide by D |
| B (bottom left) | B = (A times D) / C | Multiply A and D, divide by C |
| C (top right) | C = (A times D) / B | Multiply A and D, divide by B |
| D (bottom right) | D = (B times C) / A | Multiply B and C, divide by A |
Quick sanity-check examples you can verify by hand
| Proportion | Solve for | Answer |
|---|---|---|
| 3/4 = x/20 | x | 15 |
| 2/5 = 8/x | x | 20 |
| x/9 = 4/6 | x | 6 |
| 6/8 = 9/x | x | 12 |
Common mistakes to avoid
- Multiplying straight across instead of diagonally. Cross multiplication pairs each top number with the opposite bottom number. A goes with D and B goes with C. Multiplying A by B or C by D instead is the most frequent slip and gives a wrong answer.
- Leaving more than one box blank. A proportion has one unknown at a time. If two or more boxes are empty there is no single solution, so fill in three values and leave exactly one blank.
- Mixing up the order of the two ratios. Keep the same unit on top in both fractions. If the left ratio is servings over eggs, the right ratio must also be servings over eggs, not eggs over servings.
- Forgetting that a zero denominator has no answer. If solving would force a division by zero, the proportion has no valid result. Check that the value acting as the divisor is not zero.
Glossary
- Ratio
- A comparison of two quantities, such as 3 to 4, often written as a fraction 3/4.
- Proportion
- A statement that two ratios are equal, for example A/B = C/D.
- Cross multiplication
- A method for solving a proportion by multiplying each numerator by the opposite denominator, giving A times D = B times C.
- Numerator
- The top number of a fraction.
- Denominator
- The bottom number of a fraction. It can never be zero.
- Unknown
- The single value you are solving for, often labelled x.
Frequently asked questions
What is a proportion?
A proportion is an equation stating that two ratios are equal, written as A divided by B equals C divided by D. It means both pairs of numbers share the same relationship at a different scale.
How does this calculator solve for x?
It uses cross multiplication. From A/B = C/D it forms A times D = B times C, then rearranges the equation so the blank value stands alone, multiplying the two known diagonals and dividing by the remaining known number.
Which box should I leave blank?
Leave blank whichever value you want to find. Fill in the other three boxes with the numbers you know, then press Solve. Exactly one box must be empty.
Can I use decimals or negative numbers?
Yes. The calculator accepts whole numbers, decimals, and negative values. The only case it cannot solve is when the answer would require dividing by zero.
Why does it say there is no answer?
That message appears when solving the proportion would require dividing by zero, which is undefined. Check that the value acting as the divisor in your case is not zero.
Is my data sent anywhere?
No. The entire calculation runs in your browser using plain JavaScript. Nothing you type is uploaded or stored on a server.