Normal Distribution Calculator
Find the normal density and cumulative probability at a value, drawn as a curve.
What is Normal Distribution?
The normal distribution is the bell curve: symmetric about its mean, with a spread set by its standard deviation. About 68% of values fall within one σ of the mean and about 95% within two, which is why it models so many natural measurements.
How it works
The cumulative probability is computed from an erf approximation accurate to better than 1.5 × 10⁻⁷, and the whole left tail is shaded on an inline SVG drawn from the live mean and σ. The PDF value, both tail areas and the equivalent percentile are reported together.
- Enter your input. Type or paste your input into the field above — the tool responds instantly.
- Review the result. Output updates live as you type. Everything runs entirely in your browser.
- Copy or download. Use the Copy button to grab the result, or Download to save it as a file.
Examples
Realistic sample
Type or paste any realistic input — the tool computes the result locally and instantly.
Common mistakes
Expecting a server round-trip
Nothing is uploaded — every tool in this category runs entirely in your browser.