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Normal distribution probability
Approximate the probability below a value (CDF error about 1.5×10⁻⁷).
Enter the threshold, distribution mean and positive standard deviation. The calculator standardizes the threshold and uses an error-function approximation to return probabilities below and above it.
How to use
- Enter your text, values, or image.
- Adjust the options and run the tool.
- Copy or download your result.
Worked example
Example input
Threshold: 0 Mean: 0 Standard deviation: 1
Example result
{
"z": 0,
"below": 0.5,
"above": 0.5
}Limitations and details
Assumes a normal distribution; the CDF is approximate, with about 1.5 × 10⁻⁷ absolute error, and extreme tails may round to zero.
Inputs and options
- Threshold
- Number
- Mean
- Number
- Standard deviation
- Number
Frequently asked questions
Is this tool free and private?
Yes. All 300 tools are free in this phase. Processing happens in your browser; your input and files are not sent to our servers.