Updated
Using Normal distribution calculator
Find lower-tail and upper-tail probabilities for a normal distribution from its mean and standard deviation.
Assumes the specified normal distribution is an appropriate model. Density is not the probability at one exact value. Numerical integration supports normal scores from −37.5 to 37.5. Lower and upper tails are computed separately to preserve small probabilities; a rounded cumulative value can still display as 1.
A worked example
With value x = 1, distribution mean = 0, standard deviation = 1, the probability at or below x (percent) is 84.13447460685428.
Before you use the result
Assumes the specified normal distribution is an appropriate model. Density is not the probability at one exact value. Numerical integration supports normal scores from −37.5 to 37.5. Lower and upper tails are computed separately to preserve small probabilities; a rounded cumulative value can still display as 1.
Example results for value x
These examples use Distribution mean: 0; Standard deviation: 1. They are reference calculations, not recommended settings.
| Value x | Probability at or below x (percent) |
|---|---|
| 0.5 | 69.1462461274 |
| 1 | 84.1344746069 |
| 2 | 97.7249868052 |
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ToolOctopus. “Normal distribution calculator.” Updated 2026-09-26. https://tooloctopus.com/normal-distribution-calculator.
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