Normal Distribution Calculator
Find probabilities for any normal distribution. Enter the mean and standard deviation, then compute the chance of a value being below, above, or between given points.
Distribution (standardized)
0.8413What is the normal distribution?
The normal (or Gaussian) distribution is a symmetric, bell-shaped distribution described entirely by its mean and standard deviation. Many natural measurements — heights, test scores, measurement errors — are approximately normal, which makes it the most important distribution in statistics.
The empirical rule says about 68% of values lie within one standard deviation of the mean, 95% within two, and 99.7% within three.
How the probabilities are found
To find a probability, the calculator standardizes your value into a z-score, z = (x − μ) / σ, then reads the area under the standard normal curve. P(X < x) is the area to the left, P(X > x) is the area to the right, and P(a < X < b) is the area between the two z-scores.
Normal probabilities in Excel
Use =NORM.DIST(x, mean, standard_dev, TRUE) for P(X < x). For P(X > x), subtract that from 1. For P(a < X < b), subtract NORM.DIST(a, …) from NORM.DIST(b, …).
Frequently asked questions
How do I find the probability between two values?
Convert both values to z-scores, find the cumulative probability for each, and subtract the smaller from the larger. The result is P(a < X < b). This calculator does it for you when you choose the "between" option.
What is the difference between the normal and standard normal distribution?
The standard normal distribution is a normal distribution with a mean of 0 and a standard deviation of 1. Any normal distribution can be converted to it by standardizing values into z-scores.
What are the mean and standard deviation of a normal distribution?
The mean sets the center of the bell curve, and the standard deviation sets its spread. Together they completely define a normal distribution.