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. The area to the left of z gives the probability of falling below x, the area to the right gives the probability of falling above x, and subtracting one shaded area from another gives the probability of falling between two values.
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. It's a quick sanity check: if your calculated probability for one standard deviation isn't close to 0.68, double-check your mean and standard deviation.
Does this use z or t?
The normal distribution calculator uses the normal (z) distribution. For small samples where the population standard deviation is estimated, a t-distribution is more appropriate. This calculator assumes the standard deviation you enter is the true population value, so it always applies the z (normal) distribution.
Is my data sent anywhere?
No — the normal distribution calculator runs entirely in your browser using JavaScript, with no server round-trip. Your mean and standard deviation are never uploaded, logged or stored. The tool keeps working without an internet connection.