Random Number Generator, Normal Distribution
Draw values that follow a normal distribution with the mean and standard deviation you set.
Normal Distribution Generator
Mean 0, sd 1
Distribution
How many values
How to use the normal distribution generator
- Set the mean, the standard deviation and the decimal places.
- Generate a batch. The sample mean and standard deviation show alongside.
- Copy or export the values.
What is a normal distribution generator
A normal distribution generator draws values that follow a bell curve, using the mean and standard deviation you set rather than a flat range. Enter your mean, your standard deviation and how many values you need, and Random Nr returns numbers clustered around the mean and thinning out at the edges, which is what statistics work, simulations and realistic test data call for.
What is the 68 95 99.7 rule
A normal distribution spreads values in a bell shape around the mean, and a fixed share falls within each band of standard deviations. This is the famous 68, 95, 99.7 rule.
| Within | Share of values | For mean 100, sd 15 |
|---|---|---|
| 1 standard deviation | 68% | 85 to 115 |
| 2 standard deviations | 95% | 70 to 130 |
| 3 standard deviations | 99.7% | 55 to 145 |
So with a mean of 100 and a standard deviation of 15, the classic IQ scale, about two thirds of values land between 85 and 115, and virtually all within 55 to 145. Generate a large batch here and the counts settle onto these shares.
How normal distribution values are generated
This tool uses the Box Muller transform, which turns two uniform random numbers from the cryptographic source into a pair of independent values that follow a normal distribution. Each result is then scaled by your standard deviation and shifted by your mean. Unlike a uniform draw, where every value in a range is equally likely, a normal draw concentrates values near the mean and thins them toward the tails.
What the sample mean and standard deviation show
For each batch the tool shows the sample mean and standard deviation, which sit close to the values you set and get closer as the batch grows, a direct demonstration of the law of large numbers. For a flat spread instead of a bell, the random number generator draws uniformly, and the decimal generator adds precision control.
More number generators
Frequently asked questions
What is a normal distribution
A bell shaped spread where values cluster around a central mean and thin out toward the edges. Heights and measurement errors often follow it.
What do mean and standard deviation do
The mean sets the centre and the standard deviation sets the width. A larger standard deviation spreads the values wider.
How are the values generated
With the Box Muller method, which converts uniform random numbers from the browser cryptographic source into normally distributed ones.
Can the values be negative
Yes. A normal distribution extends both ways from the mean, so with a mean of 0 you will see negative and positive values.
Is it free
Yes, free and with no sign up.
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For a flat spread instead of a bell curve, use the random number generator, or draw a fair sample with the random sample generator.