Statistics

Normal Distribution Calculator

Calculate probabilities and values for the normal (Gaussian) distribution

Calculate*

Mean (μ)*

Standard Deviation (σ)*

X Value

Probability

Z-Score

1.5000

The standardized normal value

P(X ≤ x)

0.933193

P(X > x)

0.066807

Probability Density f(x)

0.129518

Height of the normal curve at x

Z = (x − μ) / σ
P(X ≤ x) = Φ(z)  [normal CDF]
PDF = (1 / σ√(2π)) × e^(−(x−μ)²/2σ²)

Supported inputs

Input	Description
Calculate	prob_from_x · x_from_prob
Mean (μ)	The mean of the normal distribution
Standard Deviation (σ)	Must be greater than 0
X Value	The value for which to calculate the probability
Probability	Enter a value between 0 and 1

Formula

Z = (x − μ) / σ
P(X ≤ x) = Φ(z)  [normal CDF]
PDF = (1 / σ√(2π)) × e^(−(x−μ)²/2σ²)

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