Direct
Prices and quantities
If 3 kg cost $150, then 7 kg cost $350.
Math
Rule of three calculator
Find the unknown value in direct and inverse proportions with a result, verification and step-by-step work.
Set up the proportion
Enter three known values. The calculator finds the fourth value and shows how it reached the result.
Quantity 1 Quantity 2
X
If A corresponds to B, then C corresponds to X.
Publicidad
Step-by-step work
The calculation updates in real time and keeps the work visible so you can review the setup.
- Complete the values to view the steps.
Common examples
These situations show when direct or inverse proportions are commonly used.
Inverse
Workers and time
If 4 workers take 12 days, then 6 workers take 8 days.
Direct
Recipes
If 2 cups serve 5 portions, 8 portions need 3.2 cups.
Direct rule of three
Use it when both quantities change in the same direction. If one increases, the other also increases; if one decreases, the other also decreases.
Formula: X = (B × C) / A
Inverse rule of three
Use it when one quantity increases as the other decreases. It is common in problems involving workers, time, speed or productivity.
Formula: X = (A × B) / C
Educational notice
This calculator is an educational tool. The result depends on the entered values actually forming a direct or inverse proportion. If unsure, review the steps and verification before using the result.
Frequently asked questions
What is the rule of three?
The rule of three is a method for finding a fourth value when three related values in a proportion are known.
View Spanish rule-of-three guideWhat is the direct rule-of-three formula?
If A corresponds to B and C corresponds to X, the direct formula is X = (B × C) / A.
What is the inverse rule-of-three formula?
If A corresponds to B and C corresponds to X, the inverse formula is X = (A × B) / C.
How do I know whether a proportion is direct or inverse?
It is direct when both quantities rise or fall together. It is inverse when one increases as the other decreases, such as workers and days needed to finish a task.
Can I use decimals or negative values?
Yes. The calculator accepts decimal points or commas. Negative values are allowed, but a warning asks you to confirm they make sense in context.