Direct and inverse, with the working shown. Free, nothing to install, no sign-up.
The rule of three solves the commonest problem of all: you know three numbers and you are missing the fourth. This calculator does both kinds, direct and inverse, and shows the working so you can copy it. Pick the kind with the two buttons at the top, enter the three numbers you have and it gives you the one that is missing. It runs inside your browser and downloads as a PDF.
It is direct when one going up makes the other go up too: more kilos of apples, more money. It is inverse when one going up makes the other go down: more workers, fewer days to finish the job. Before you touch a single number, say the sentence out loud with "more" and "more" or with "more" and "fewer". That sentence decides the whole sum, and it is where everyone goes wrong.
If 3 kilos cost 6, what do 5 kilos cost? You multiply the two numbers that sit diagonally and divide by the one left over: 5 × 6 ÷ 3 = 10. The shortcut is to work out what ONE costs first: 6 ÷ 3 = 2 per kilo, and 2 × 5 = 10. Same answer, and putting the unit first makes it much harder to get muddled.
If 4 workers take 6 days, how long do 3 workers take? Here you do not multiply diagonally, because fewer workers does not mean fewer days. What stays constant is the TOTAL WORK: 4 × 6 = 24 worker-days. With 3 workers, 24 ÷ 3 = 8 days. The rule is: in the inverse kind you multiply the two that belong together and divide by the third.
Look at the answer and ask whether it goes the way you expected. Ask for more kilos and the price has to come out higher; put in fewer workers and the days have to come out longer. If the answer runs against common sense, you did not slip in the arithmetic — you picked the wrong kind. Go back to the "more and more" or "more and fewer" sentence.
Say the relationship out loud: "if there is more of this, is there more or less of that?". More kilos, more money: direct. More taps, less time to fill the pool: inverse. There is no other trick, and skipping that sentence is where nearly every mistake starts.
Yes, and it is a handy way to see them. "If 80 is 100%, what is 20%?" is a direct rule of three: 20 × 80 ÷ 100 = 16. If you work with percentages a lot the percentage calculator is quicker to hand, but the reasoning is identical.
That is a compound rule of three, and you solve it in stages: hold one quantity still, solve the rule of three for the other two, then repeat with the one you held. This calculator does the simple kind, which is what most problems are.
No. It runs entirely inside your browser: the numbers never leave your device and are not stored anywhere. No account, no email address.
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