The rule of three (or cross multiplication) finds an unknown fourth value from three known values when two quantities are proportional. This calculator solves both the direct rule of three (when both quantities grow or shrink together) and the inverse rule of three (when one grows while the other shrinks), and it accepts decimals with either a comma or a dot.
Along with the result, it shows the full working: the formula used and the numbers plugged in, so it also helps you understand the calculation rather than just handing you a final figure.
How to use
- 1Choose whether the proportion is direct (more means more) or inverse (more means less).
- 2Enter A and B, the pair of values you already know.
- 3Enter C, the value you want to find the match for.
- 4Read the result X and the step-by-step working.
What you can do
- Direct and inverse proportions
- Step-by-step working
- Supports decimals
Direct vs. inverse proportion
In a direct proportion, both quantities move together: if one increases, so does the other, in the same ratio. For example, if 3 kg of apples cost $9, 5 kg will cost more, using the formula X = (C × B) ÷ A.
In an inverse proportion, the quantities move in opposite directions: if one increases, the other decreases. For example, the more workers on a job, the fewer days it takes to finish, using the formula X = (A × B) ÷ C.
Common examples
The rule of three shows up in all kinds of everyday and school situations:
- Converting prices: if 2 kg costs $10, how much do 3.5 kg cost?
- Scaling a recipe up or down for more or fewer servings.
- Working out how long several workers will take to finish a task.
- Adjusting quantities of ingredients, materials or doses proportionally.
Common mistakes
The most common mistake is mixing up direct and inverse: ask yourself whether, as A increases, B should also increase (direct) or decrease (inverse) in the real situation you are modeling. Another common issue is dividing by zero when A or C is zero, which has no mathematical solution — this calculator detects that and warns you instead of showing a wrong result.
Frequently asked questions
How do I know if a proportion is direct or inverse?
It is direct when, in the real situation, increasing one quantity also increases the other (more kilos, more cost). It is inverse when increasing one decreases the other (more workers, fewer days).
Can I use decimals?
Yes. You can type the three values with a comma or a dot as the decimal separator, such as “2.5” or “2,5”; the calculator reads them the same way.
What happens if A or C is zero?
The formula would need to divide by zero, which has no mathematical solution. The calculator detects this and shows a warning instead of an incorrect result.
Does this solve the compound rule of three?
No: this tool solves the simple rule of three, with a single quantity related to the result. The compound rule of three, with several quantities at once, needs a different calculator.