VastCalc
Statistics
Normal Distribution Calculator
Calculate probabilities and z-scores for the normal distribution. Find P(X < x), P(X > x), and P(a < X < b) given mean and standard deviation.

Normal Distribution Calculator

Calculate probabilities for the normal (Gaussian) distribution. Find the probability that a value falls below, above, or between two points on the bell curve.

The normal distribution (bell curve) is the most important distribution in statistics.

PDF (Probability Density Function): f(x) = (1 / (σ√(2π))) × e^(-(x-μ)²/(2σ²))

CDF (Cumulative Distribution Function): P(X ≤ x) = Φ((x - μ) / σ)

where Φ is the standard normal CDF.

68-95-99.7 Rule:

  • 68% of data falls within 1σ of the mean
  • 95% within 2σ
  • 99.7% within 3σ

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