Use this when one value goes up while the other goes down. Add a known pair, enter a new value, get X with a quick check.
You give one known pair. You give the new first value. The tool returns the new second value.
Example: 4 workers finish in 6 days.
This is the changed first value. In an inverse relationship, more A usually means less B.
If the relationship is inverse, the products match: \(A \times B\) should equal \(C \times X\).
You will see X plus a product check. Copy the number if you need it.
Pick one, then edit values.
You can solve the arithmetic and still solve the wrong problem.
The inverse rule of three is for pairs where one goes up while the other goes down. People mix it with direct proportion because both use the same four symbols on paper.
This page uses a single rule: the product is constant.
Known pair: \(A\) with \(B\). New case: \(C\) with \(X\).
\(A \times B = C \times X\)
\(X = \frac{A \times B}{C}\)
After calculation, the page shows both products so you can verify the match.
Inverse proportion is practical. Here are common setups.
Same job size. More workers, fewer days.
If 4 workers take 6 days, 8 workers take 3 days.
Same distance. Higher speed, less time.
At 60 mph the trip is 4 hours. At 80 mph it becomes 3 hours.
Same tank. More pipes, fewer hours.
If 3 pipes fill a tank in 8 hours, 6 pipes take 4 hours.
If your setup looks like a ratio problem instead, use the cross multiplication calculator or a proportion tool.
Some problems feel inverse but do not need a full rule-of-three setup.
If A doubles, B halves. If A becomes 1.5 times, B becomes \(1 \div 1.5\) times. This is quick for mental math.
If more input leads to more output, skip inverse. Use single rule of three direct.
This calculator assumes a clean inverse relationship. Real life sometimes refuses that assumption.
If you suspect a direct relationship, start with the direct rule tool. If you need a matrix workflow instead, see the matrix calculator.
The method is the inverse proportion identity. The calculation is client-side. Your numbers stay in your browser tab.
Formula: \(X = (A \times B) \div C\). Validation: products match within a tiny tolerance after rounding.
