Rule of three
Simple rule of three, direct and inverse, with the working explained.
Fill in three values and find the fourth. Use the direct rule when quantities grow together (more kilos, more cost) and the inverse when one grows as the other falls (more people, less time). The tool shows the assembled calculation, so you can check the reasoning, not just the number.
How to use
- Pick the type: direct (both grow together) or inverse (one grows as the other falls).
- Fill in the three known values.
- x is filled in, with the formula used shown below.
How the simple rule of three works
It solves proportions: you know three values and want the fourth. In the form a is to b as c is to x, the direct rule cross-multiplies — x = (b × c) ÷ a. If 3 kg of rice costs 12, then 5 kg costs (12 × 5) ÷ 3 = 20.
When the rule is inverse
Some quantities move in opposite directions: more workers, fewer days; more speed, less time. Then you multiply horizontally — x = (a × b) ÷ c. If 4 people finish a job in 6 days, 8 people take (4 × 6) ÷ 8 = 3 days.
Quick test: if I increase the first value, should the answer go up or down? If down, it is inverse.
Where it shows up
Scaling recipes, paint for a bigger wall, map scales, currency conversion and dosage adjustments are all direct. Delivery time per machine and fuel use per speed tend to be inverse. To convert between different units, the unit converter already has the factors.
Frequently asked questions
When do I use the inverse rule?
When increasing one quantity decreases the other: more workers on the same job means fewer days; more speed means less travel time. In the direct rule, both grow together.
How is the calculation assembled?
Direct: cross multiply, x = (b × c) ÷ a. Inverse: multiply horizontally, x = (a × b) ÷ c. The tool prints the formula used under the result.
Does it work for recipes and ingredient ratios?
Yes, and that is one of the most common uses. If a recipe serves 8 with 500 g of flour and you want 12 servings, the direct rule gives the proportional amount.