Normal Distribution Calculator
Calculate probabilities for normal distributions. Convert between z-scores and raw values.
Normal Distribution Curve
Results
1
x value
1
z-score
84.13%
Percentile
P(X < x): 84.1345%
P(X > x): 15.8655%
Empirical Rule (68-95-99.7)
68% within 1σ:[-1, 1]
95% within 2σ:[-2, 2]
99.7% within 3σ:[-3, 3]

Normal Distribution

z = (x - μ) / σ
φ(z) = (1/√2π)e^(-z²/2)

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