Normal Distribution Calculator
Evaluate density and tail areas for a normal distribution.
How the normal distribution calculator works
A normal distribution is determined by its mean and positive standard deviation. Standardizing x gives the z score, density measures curve height at that point, and the cumulative distribution gives area to the left. This calculator evaluates all four related quantities with the Gaussian density formula and a numerical error-function approximation, while keeping density distinct from probability.
The defaults use the standard normal distribution with mean zero, standard deviation one, and x equal to one. The verified density is approximately 0.2419707245 and the cumulative probability is approximately 0.8413447461. Thus about 84.13 percent lies below one, while about 15.87 percent remains in the upper tail.
Reading normal distribution calculator results privately
Density at a point is not the probability of that exact continuous value; probabilities come from areas over intervals. The error-function approximation is accurate for ordinary use but not a substitute for specialized high-precision statistical software. A normal model is appropriate only when its shape and assumptions fit the data-generating process being studied. This normal distribution calculator calculation runs entirely in your browser, so the numbers you enter never leave your device.
Frequently Asked Questions
What is the difference between density and cumulative probability?
Density is curve height at x. Cumulative probability is the total area under the curve from negative infinity through x.
Why must standard deviation be positive?
Zero spread would collapse the continuous distribution to a point and make the normal density formula divide by zero.
Is the normal distribution calculator private?
Yes. Its inputs and results stay in your browser. Bushe.co does not upload or store the values used in this calculation.
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