How are the numbers generated?

The tool uses the Box-Muller transform, which converts two independent uniform random values into a standard normal value, then scales and shifts it by your standard deviation and mean.

Why does the sample mean not exactly equal my chosen mean?

Random samples fluctuate around the true mean. With small sample sizes the sample mean and standard deviation can differ noticeably; they converge toward your inputs as the sample size grows.

What values are allowed?

The mean can be any real number, the standard deviation must be greater than zero, and the count must be a whole number between 1 and 1000. Invalid inputs are rejected with a message.

What is a normal distribution used for?

The normal or Gaussian distribution models many natural quantities such as measurement error, heights, and test scores. These samples are useful for Monte Carlo simulations, statistics teaching, and seeding test data.

Are the numbers cryptographically secure?

No. They come from the browser's Math.random generator, which is fine for simulations and testing but should not be used for cryptography or anything security-sensitive.

Gaussian Random Number Generator

Sample from a bell curve on demand

While most random tools give you uniform numbers, real-world quantities like measurement noise, heights, or returns tend to follow a normal (Gaussian) distribution. This generator produces values clustered around a mean you choose, with a spread set by the standard deviation — perfect for simulations, statistics lessons, and generating realistic-looking test data.

How it works

Uniform random numbers cannot be reshaped into a bell curve by simple scaling, so the tool uses the classic Box-Muller transform. It draws two independent uniform values U1 and U2 in the range (0, 1) and computes a standard normal value:

z = sqrt(-2 * ln(U1)) * cos(2 * pi * U2)

This z has mean 0 and standard deviation 1. Each sample is then shifted and scaled to your parameters with x = mean + stdDev * z. After generating the requested count of samples, the tool reports the sample mean, the sample standard deviation (using the unbiased n − 1 divisor), and the minimum and maximum so you can confirm the output matches the distribution you asked for.

Tips and notes

Generate a large sample, such as several hundred values, to see the sample mean and standard deviation closely match your inputs — small samples will wander more. About 68 percent of values should land within one standard deviation of the mean and roughly 95 percent within two, a quick sanity check you can perform on the output. These numbers rely on Math.random() and are suitable for modelling and testing, but not for cryptographic use.