Normal Distribution PDF Calculator
Evaluate the normal probability density at x.
Open toolNormal Distribution CDF Calculator
Estimate the normal probability P(X ≤ x). Positive standard deviation.
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Enter the inputs, then select Calculate.
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How Normal Distribution CDF Calculator works
Estimate the normal probability P(X ≤ x).
Positive standard deviation. Uses an erf approximation with absolute error below about 1.5 × 10⁻⁷; it is not an exact tail-probability calculation. Finite real inputs; output uses up to 12 significant digits. Floating-point results may be rounded.
How to use Normal Distribution CDF Calculator
Follow the labelled inputs.
Enter value x
Replace the example with value x. The field labels specify the expected format and units.
Input and settings
Tool result
Run, review and save
Select Calculate. Review the calculated result, then copy it or download the result text.
Review the details
Examples and uses for Normal Distribution CDF Calculator
Check the supplied example
The starting example produces 0.5. Estimate the normal probability P(X ≤ x).
Use your own inputs
Read the labels for value x and mean, standard deviation. Positive standard deviation.
Record a reviewed result
Copy the calculated result into your notes. Keep the formula and assumptions with it if someone else needs to reproduce the calculation.
How to read the result
Read the units and assumptions with the output.
Estimate the normal probability P(X ≤ x).
Positive standard deviation. Uses an erf approximation with absolute error below about 1.5 × 10⁻⁷; it is not an exact tail-probability calculation. Finite real inputs; output uses up to 12 significant digits. Floating-point results may be rounded.
Supported input and limits
Check the stated scope before you run it.
Positive standard deviation. Uses an erf approximation with absolute error below about 1.5 × 10⁻⁷; it is not an exact tail-probability calculation. Finite real inputs; output uses up to 12 significant digits. Floating-point results may be rounded.
The input stays in this browser. Copy result and Download save the same displayed text.
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Open toolNormal Distribution CDF Calculator: common questions
Answers about using Normal Distribution CDF Calculator and understanding its results.
What assumptions and input limits apply?
Positive standard deviation. Uses an erf approximation with absolute error below about 1.5 × 10⁻⁷; it is not an exact tail-probability calculation. Finite real inputs; output uses up to 12 significant digits. Floating-point results may be rounded.
How can I save the output?
Use Copy result to copy the displayed text, or Download to save it as a text file. The tool runs in your browser and does not require an account.
Calculate with your input
Check the calculated result, then copy or download it.