Solve any position
Leave A, B, C or X empty and the calculator detects the unknown and cross-multiplies to fill it in — no need to rearrange the formula yourself.
Cross-multiplication · Direct & inverse · Compound · Step-by-step · No upload
Rule of Three Calculator
Enter three values of a proportion and leave the fourth blank — the calculator cross-multiplies and fills it in instantly, showing the exact working. Switch to inverse when one quantity rises as the other falls (speed and time, workers and days), or to compound when several factors act at once. Set how many decimals you want and read the formula it used. Everything runs in your browser — no upload, no sign-up.
Leave exactly one box empty. Direct: A is to B as C is to X.
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Each factor column scales the result. Mark a column Direct (grows together) or Inverse (one up, other down). Leave the bottom result blank.
Factor columns:
Result
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Ready
Key features
Direct & inverse
One click switches between proportions that grow together and inverse ones where a bigger cause means a smaller result, like speed versus travel time.
Compound rule of three
Add up to three factor columns, each set to direct or inverse, to solve real problems with workers, days, output or distance in a single step.
Working shown
Every answer comes with the exact line of arithmetic used, so it doubles as a study aid for homework and exam practice.
Frequently asked questions
What is the rule of three?
The rule of three solves a proportion when three of its four values are known. You write the equality a/b = c/x and cross-multiply, so x = b × c ÷ a. It is the quickest way to scale a quantity up or down while keeping the ratio fixed — recipes, prices, map distances and currency conversions all use it.
How does cross-multiplication work?
Set the problem up as two equal fractions. Multiply the two numbers that sit diagonally across from each other, then divide by the remaining known value. For 2/10 = 5/x the diagonal product is 10 × 5 = 50, divided by 2 gives x = 25. The calculator highlights which value it solved for and prints this line.
When should I use the inverse rule of three?
Use it whenever one quantity goes up as the other goes down so that their product stays constant. If 4 workers finish a job in 6 days, 8 workers finish it in 3 days — twice the workers, half the time. In inverse mode the tool multiplies across each row (a × b = c × x) instead of diagonally.
What is the compound rule of three?
It handles a proportion with more than one cause. For example: if 4 workers build 3 walls in 12 days, how many days do 6 workers need for 5 walls? Each factor (workers, walls) is marked direct or inverse against the result, and the calculator combines all the ratios at once.
Is my data sent anywhere?
No. All arithmetic happens locally in your browser. Nothing is uploaded, and the page keeps working offline once it has loaded.