Normal Cdf Calculator
Compute the cumulative distribution function (CDF) for a normal distribution with given mean and standard deviation.
Published by:
isCalculator Editorial Team
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How to use this tool?
This calculator computes the cumulative distribution function (CDF) for a normal distribution: the probability that a random variable X is less than or equal to a given value x, written as P(X ≤ x).
- Enter the Mean (μ) – the average of your normal distribution.
- Enter the Standard Deviation (σ) – must be a positive number (e.g., 1, 2.5).
- Enter the Value (x) – the cutoff point for which you want the probability.
- Click Calculate CDF or press Enter on any input field.
The result shows the probability as a decimal between 0 and 1 (e.g., 0.841345). The formula used is Φ((x − μ) / σ), where Φ is the standard normal CDF.
Tip: All inputs accept decimals. Ensure σ > 0 to avoid an error.
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Frequently Asked Questions
The normal cumulative distribution function (CDF) gives the probability that a normally distributed random variable is less than or equal to a given value.
The calculator uses the standard normal CDF approximation formula (Abramowitz and Stegun) after standardizing the input value.
You need to provide the mean (μ), standard deviation (σ), and the value (x) for which to compute the CDF.
