Gaussian (Normal Distribution) Random Number Generator — Free
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Uniform randomness is the wrong model for most natural variation — heights, measurement noise, and test scores cluster around an average. This generator draws from a normal (Gaussian) distribution with the Box–Muller transform: set the mean and the standard deviation, choose how many draws you want, and get values that cluster realistically around the mean.
How it works
- 1
Set the distribution
Mean (the center of the bell curve) and standard deviation (how wide it spreads).
- 2
Choose how many draws
A single value or up to a thousand at once.
- 3
Generate and copy
Results appear to six decimal places; one click copies the whole list.
About this tool
What makes Gaussian different
Uniform randomness is flat — every value in range equally likely. Gaussian (normal) randomness clusters around a mean with symmetric spread, the distribution of real measurements: heights, measurement errors, delivery times, test scores. The tool produces these samples with the mean and spread you set.
Where the bell curve appears
Simulating realistic test data (uniform test data looks fake; Gaussian data looks measured), sampling for statistics exercises, modeling noise in signals, and Monte Carlo experiments. Anywhere real-world variation is the subject, the bell curve is the model.
Mean and spread
The mean is the center the values cluster around; the standard deviation is the typical distance from that center — about 68 percent of samples land within one deviation, 95 within two. Set them to match the phenomenon you are modeling.
Frequently asked questions
Can the generator produce negative values?
Yes — a Gaussian with a small mean and large deviation reaches below zero naturally. Shift the mean up or clamp the results if negatives make no sense for your model.
Why do my samples cluster near the mean?
That is the definition of the distribution — values near the mean are common, extremes rare. If you wanted flat clustering, use a uniform generator instead.
What are the values used for?
Anything modeled by the bell curve: simulated measurements, noise samples, test inputs with realistic spread, statistical demonstrations.