Rule of Three Calculator (Direct Proportion) — Free
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The rule of three solves the everyday proportion: if A corresponds to B, what does X correspond to? Prices, recipes, fuel consumption, unit conversions — anywhere two quantities grow together. Type the three values you know and the fourth appears instantly, with the proportion spelled out above the answer.
How it works
- 1
Enter the known pair
Value A and the value B that corresponds to it — for example, 3 items and $6.
- 2
Enter the third value
The amount you want to find the counterpart for — for example, 5 items.
- 3
Read the fourth value
The answer appears live, with the full proportion restated so you can sanity-check it.
About this tool
The proportion, solved
If A corresponds to B, then C corresponds to — the tool fills in the fourth value of the direct proportion: more of one thing means proportionally more of the other. Three knowns in, the fourth out, no cross-multiplication arithmetic to fumble.
The direct cases
Price per quantity (5 apples cost 3 dollars — what do 12 cost?), distance and time at constant speed, recipe scaling, unit conversions built on ratios, and any relationship where doubling one side doubles the other. Direct proportion is the most-used mental model in daily arithmetic.
Check the relationship first
The rule of three assumes the relationship is truly proportional — no fixed fees, no bulk discounts, no step changes. If doubling the input does not quite double the output, the proportion is only approximate, and the answer is an estimate, not an exact.
Frequently asked questions
How do I know my relationship is proportional?
Test it: doubling one side should double the other. A delivery that costs 10 for one package and 15 for two is not proportional — there is a fixed component.
What units work here?
Any consistent pair — the proportion is about the relationship. Enter both values in the same unit system and the result carries the same units.
Can the values be decimals?
Yes — proportions work in full decimal precision, which is often where hand arithmetic slips and the tool does not.