Ratio Calculator · Practical guide
How to Solve for x in a Proportion
Cross-multiply: for A : B = C : D, the equation A × D = B × C isolates whichever value is missing.
At a glance
Quick answer
To solve for x in a proportion, cross-multiply: for A : B = C : D, multiply the diagonals to get A × D = B × C, then divide to isolate x. In 3 : 4 = x : 20, that gives 3 × 20 = 4x, so 4x = 60 and x = 15. Enter any three values above, leave x blank, and the calculator solves it instantly.
Interactive tool
Ratio Calculator
Enter your own values, then compare the result with the examples below.
Proportion: A : B = C : D (leave one field blank to solve)
Result
Step-by-Step: 3 : 4 = x : 20
- Cross-multiply the diagonals: A × D = B × x, so 3 × 20 = 4x.
- Simplify: 60 = 4x.
- Divide both sides by 4: x = 15.
- Check: 15 : 20 simplifies to 3 : 4 (divide both by 5), so the proportion holds.
Missing Value in Any Position
The same diagonal rule isolates whichever term is unknown:
| Proportion | Setup | Answer |
|---|---|---|
| 2 : 5 = x : 15 | x = (2 × 15) ÷ 5 | x = 6 |
| 4 : 7 = 12 : x | x = (7 × 12) ÷ 4 | x = 21 |
| x : 6 = 10 : 15 | x = (6 × 10) ÷ 15 | x = 4 |
| 9 : x = 27 : 10 | x = (9 × 10) ÷ 27 | x = 3.3333 |
Always Verify by Simplifying
A quick check catches arithmetic slips: both sides of a true proportion reduce to the same simplest ratio. For 4 : 7 = 12 : 21, the right side divides by 3 to give 4 : 7 — confirmed. The calculator shows the simplified ratio and the scale factor (here, 12 ÷ 4 = 3) alongside every answer, so verification is built in.
Decimals Are Fine
Proportions are not limited to whole numbers. For 2.5 : 4 = x : 10, cross-multiply to get 4x = 25, so x = 6.25. The calculator handles decimals and fractions to six decimal places.
Frequently Asked Questions
Which diagonal do I multiply first?
Either one — cross-multiplication multiplies both diagonals and sets them equal: A × D = B × C. The missing term is then isolated by dividing.
What if x is in both ratios?
This calculator solves proportions with a single unknown. If x appears twice, rearrange the equation into a linear or quadratic equation first.
Can a proportion have a zero in it?
A zero term usually breaks the proportion because division by zero is undefined. In practice, if A = 0 then C must also be 0 for the ratios to be equal.
How is this different from cross-canceling fractions?
It is the same operation. A proportion A : B = C : D is the fraction equation A/B = C/D, and cross-multiplying clears both denominators in one step.