Inverse Rule of Three Calculator — Free
Runs 100% in your browser — your files never leave your device.
Some quantities move in opposite directions: more workers, fewer days; faster speed, less travel time. The inverse rule of three finds the missing fourth value when the product stays constant. Type the three values you know and the answer appears instantly.
How it works
- 1
Enter the known pair
Amount A and amount B — for example, 3 workers and 4 days.
- 2
Enter the new amount
The changed quantity — for example, 6 workers.
- 3
Read the result
The counterpart appears live — 6 workers take 2 days.
About this tool
The inverse proportion, solved
If A workers finish in B days, then C workers finish in — fewer workers mean more time, in exact inverse proportion. Enter three knowns and the tool computes the fourth: the product of the paired values stays constant while the individual numbers move opposite ways.
The inverse cases
Workers and completion time, speed and travel time for a fixed distance, concentration and volume in dilutions, sharing a fixed quantity among more or fewer people. The signature: when one side goes up, the other must go down for the total to stay constant.
Inverse is where intuition fails
People routinely estimate inverse proportions linearly — "double the workers, half the time" is correct, but "ten times the speed, a tenth of the time" feels extreme and is exactly right. Trust the tool over the gut; the gut models direct proportion even when the world runs inverse.
Frequently asked questions
How do I tell direct from inverse proportion?
Ask what happens when one value doubles: if the other doubles, it is direct; if it halves, it is inverse. Speed and time are the canonical inverse pair.
Does the inverse rule hold for partial participation?
Only when the resources truly pool — ten workers do not always equal one-tenth the time if coordination overhead grows. The math is exact; the real-world assumption is yours to verify.
Can I solve "how many X do I need for Y time"?
Yes — that is the same proportion with the unknown in a different position. Enter the three knowns and the tool solves for whichever value is missing.