Fundamental Counting Principle
Fundamental Counting Principle: calculate results from explicit inputs, with a formula and worked example.
Formula
- Use the units shown beside each field.
- Results update automatically whenever you change an input.
- Displayed values use up to four decimal places, or scientific notation for very small or large numbers. Calculations use standard floating-point arithmetic; exact integer and fraction tools identify their own precision rules.
- Exact integer multiplication using BigInt. Assumes every stage offers the stated number of choices for every earlier outcome.
Example Calculation
- Choices for each independent stage: 3, 4, 5
3 choices, then 4, then 5 independent choices give 3×4×5=60 outcomes.
Frequently asked questions
How do I use this calculator?
Enter choices for each independent stage. The result updates automatically. Use Reset to restore the example values.
What method does it use?
total outcomes = product of the number of choices at each stage. Exact integer multiplication using BigInt. Assumes every stage offers the stated number of choices for every earlier outcome.
Why might a rounded result differ?
The calculation keeps full numeric precision internally, then rounds the displayed result. Rounding intermediate steps by hand can produce a slightly different answer.
Are my inputs saved online?
No. This calculator processes your inputs in your browser. A recently used list stores only calculator names on this device, not your entered values.
Check the assumptions and units before using this result. Read about calculation methods.