Normal Distribution Calculator

Find the probability that a normally distributed value falls below, above or between given values, or find the value at a percentile.

What Do You Want to Find?
Fractions and decimals both work.
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Probability
Z-score(s)
As a percent
Complement
Work

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Normal Distribution Probabilities

z = (x − μ) ÷ σ   P(X < x) = Φ(z)   P(a < X < b) = Φ(z_b) − Φ(z_a)

The 68-95-99.7 rule: about 68% of values fall within 1 SD of the mean, 95% within 2, and 99.7% within 3.

Worked Example

Tips

For a continuous distribution, P(X < a) and P(X ≤ a) are the same. Φ is computed numerically to better than 10 decimal places.