About the Proportion Solver
What is the Proportion Solver?
A proportion is an equation stating that two ratios are equal: A : B = C : D, or A/B = C/D. When three of the four values are known, the fourth can always be found. This is the classic “rule of three” taught in school and used every day for scaling quantities.
Enter A, B and C, and the solver finds x so that A : B = C : x. It also shows the two cross products, A × x and B × C. In a true proportion they are always equal, which gives you a quick way to check the answer.
How to use the Proportion Solver
- A (in A : B = C : x) — the first term of the known ratio; it cannot be 0. (sample: 4)
- B — the second term of the known ratio. (sample: 10)
- C — the term that corresponds to A in the new situation. (sample: 6)
- Press Solve for x (results also refresh as you type). The result card shows the Value of x, along with Ratio A : B, Cross product A × x and Cross product B × C.
Formula used
x = (B × C) ÷ A
- A, B = the known ratio
- C = the first term of the second ratio
- x = the missing fourth term
This comes from cross-multiplication: A/B = C/x ⇒ A × x = B × C ⇒ x = B × C ÷ A. A cannot be zero.
Worked example
These are the sample values already filled in the calculator above, and the result it returns for them:
| Input | Sample value |
|---|---|
| A (in A : B = C : x) | 4 |
| B | 10 |
| C | 6 |
| Result | Value |
|---|---|
| Value of x | 15 |
| Ratio A : B | 0.4 |
| Cross product A × x | 60 |
| Cross product B × C | 60 |
Tips for using the Proportion Solver
- Recipe scaling: if 4 people need 250 g of rice, 6 people need x where 4 : 250 = 6 : x, so x = 375 g.
- Keep units consistent — both first terms in one unit and both second terms in another.
- If one quantity rises while the other falls (more workers, fewer days), the relationship is inverse, not direct; solve A × B = C × x instead.