Calculator Inputs and Outputs
Inputs
- Number of trials (n) — example: 10
- Exact successes (k) — example: 3
- Success probability — example: 0.5
Results
- Exact probability
- Decimal probability
- Expected successes
Formula used
P(X=k) = C(n,k)pᵏ(1−p)ⁿ⁻ᵏ.
How to Use the Binomial Probability Calculator
Enter the requested values, confirm the units and assumptions, then select Calculate Binomial Probability. The default inputs provide a working example, and the supporting outputs make the result easier to check.
Formula
P(X=k) = C(n,k)pᵏ(1−p)ⁿ⁻ᵏ.
Understanding the Results
The primary answer appears first, followed by related values, conversions, or comparisons. Calculations retain additional internal precision before the displayed result is rounded.
Accuracy Tips
- Use consistent units and measured values.
- Review whether the formula assumptions match your situation.
- For estimates, include realistic waste, efficiency, fees, or contingency values where available.
Important Note
This calculator is for informational estimation. Verify critical financial, health, construction, scientific, tax, legal, or safety decisions with an appropriately qualified professional.
Calculation Standards
This tool uses documented formulas and high-precision internal values. Displayed results may be rounded for readability. Review the assumptions and verify important decisions with a qualified professional.
Read our calculation methodology