Rule of three calculator
Solve direct or inverse proportions and see the formula used.
If A corresponds to B, what value X corresponds to C?
Your files are processed here, on your device
We do not send your file or text contents to a processing server. No account is needed and there is no daily operation quota. Individual tools have size limits to protect your device’s memory.
A connection is needed to load the site and its resources. Hosting may receive technical visit data. Favorites store only tool identifiers in this browser.
How we handle your data →How to use this tool
- Identify what A, B and C represent using consistent units.
- Choose direct or inverse according to the relationship and calculate.
- Check ratios for direct proportions and products for inverse proportions before using X.
An example you can verify
Scale a quantity or compare inversely proportional quantities.
Example input
A: 2 B: 6 C: 3
Expected result
Direct: X=9. Inverse: X=4.
Choose the type based on the actual relationship. Three people take less time than two only at the same work rate.
Rule of three calculator: uses and practical guidance
The rule of three relates two quantities under a proportionality assumption. Identify what A, B and C represent and record their units before entering them. A direct relationship retains a ratio: doubling one quantity doubles the other. An inverse relationship retains a product: doubling one quantity halves the other if other conditions remain unchanged. Choosing the correct model is part of solving the problem, not something the numeric calculation decides for you.
Do not choose direct or inverse merely because a problem contains three numbers. A cost with a fixed component does not necessarily increase proportionally with quantity. Work also may not divide perfectly among more people when coordination imposes constraints. The calculator applies the selected formula but cannot verify whether a real situation follows that model. Establish the assumption that justifies proportional reasoning before relying on the computed value.
Use consistent units. If hours and minutes describe the same quantity in different inputs, convert them before calculating. Values used as divisors must meet the stated restrictions. Check matching ratios for a direct relationship and matching products for an inverse one. This catches misplaced inputs even when every field contains a valid number. A successful calculation confirms arithmetic under the model, rather than validating how the variables were assigned.
Read the output with its unit and the problem’s conditions. Percentage calculator offers a more direct input for a percentage portion, and Unit converter handles equivalent measurements. Retain the correspondence between A and B and between C and X in your notes so another person can verify the calculation without guessing which quantity was entered in each position.
A practical check before using the result
A direct trial can use small quantities with an easily anticipated result. Then prepare an inverse example and check the products of the pairs. This verifies understanding of the model as well as the formula. Convert changed units before placing values in the form. If a problem includes a fixed component or capacity limit, consider whether proportionality remains valid across the interval. The tool does not detect those conditions itself. Write a sentence stating the assumption with the output so the calculation can be reviewed without reconstructing the problem from three isolated numbers. Arithmetic verification and assessment of the model are complementary parts of solving a proportionality exercise.
Settings and limits
If A corresponds to B, enter C to calculate X. For direct proportions, X = B × C / A. For inverse proportions, X = A × B / C. Use consistent quantities and avoid zero denominators.
Frequently asked questions
When should I use an inverse proportion?
When increasing one quantity decreases the other in the same proportion. For example, 2 people take 6 hours; 3 would take 4 hours at the same work rate.