Normal Distribution Calculator

Enter a mean and standard deviation to find the probability that a normal variable falls below, above or between values — with the area shaded on the bell curve.

Probability
As a percentage

How to Find a Normal Distribution Probability

Enter the mean and standard deviation, choose a probability type, and read the area under the curve.

1

Enter the distribution

Type the mean (μ) and standard deviation (σ) of your normal distribution.

2

Choose the probability

Pick P(X < x) for a left tail, P(X > x) for a right tail, or P(a < X < b) for a range, and enter the value(s).

3

Read the shaded area

The probability equals the shaded area under the bell curve. It is shown as a decimal and a percentage, with the z-score in the steps.

Frequently Asked Questions

How do you find a probability from a normal distribution?
Convert the value to a z-score with z = (x − μ) / σ, then read the area under the standard normal curve. This calculator does both and shades the matching region for you.
What is the empirical (68-95-99.7) rule?
For a normal distribution, about 68% of values fall within one standard deviation of the mean, 95% within two, and 99.7% within three. You can confirm it by setting the bounds to μ ± σ, μ ± 2σ and μ ± 3σ.
Does this use z or t?
It uses the normal (z) distribution. For small samples where the population standard deviation is estimated, a t-distribution is more appropriate.
Is my data sent anywhere?
No. Everything runs in your browser with JavaScript; nothing is uploaded or stored.