What you provide
What you provide
- Observation, using the same scenario as the other inputs
- Mean, using the same scenario as the other inputs
- Standard deviation, using the same scenario as the other inputs
MATH / PROBABILITY
Normal Cumulative Probability Calculator
Approximate the cumulative normal probability at an observation from a supplied mean and standard deviation. Review the equation, substituted values, result context, and modelling limits in one guided workspace.
- 01 Calculated in this tab
- 02 Values stay in this browser tab
- 03 Use boundary
Use boundary
Calculation path
Approximate the cumulative normal probability at an observation from a supplied mean and standard deviation. The page evaluates the displayed equation from your supplied values and presents both symbolic and substituted KaTeX working so the arithmetic can be checked.
Calculation pathP(X <= x) = [1 + erf((x - mu)/(sigma sqrt(2)))] / 2 Conversion resultP(X <= x) = [1 + erf((x - mu)/(sigma sqrt(2)))] / 2
What you receive
What you receive
- Probability below x from the stated equation
- A symbolic formula plus substituted working with your values
- Visible assumptions, field guidance, and an authoritative learning reference
Use boundary
Choose the maximum decimal places shown. This does not increase source accuracy.
The probability is meaningful only when a normal distribution is an appropriate model.
Use internally consistent units and retain extra precision when carrying the result into another calculation.
Reviewed reference factors