Gaussian Random Number Generator
Create normally distributed random numbers with custom parameters
Statistical Note: This generator uses the Box-Muller transform to produce accurate normal distributions. For scientific applications, verify the results meet your requirements.
Advanced Options
Generated Numbers
Sample Mean
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Sample Std Dev
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Range
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Understanding Normal Distributions
The 68-95-99.7 Rule
- 68% of values within 1σ of μ
- 95% within 2σ
- 99.7% within 3σ
Common Applications
- Natural phenomena modeling
- Quality control processes
- Financial market analysis
Generation Methodology
Box-Muller Transform
This implementation uses the Box-Muller algorithm to convert uniformly distributed random numbers into normally distributed values. The method generates pairs of independent standard normally distributed random numbers.
Cryptographic Randomness
We use the Web Crypto API for high-quality random number generation, not Math.random(). This ensures cryptographically secure results suitable for simulations and statistical modeling.
Frequently Asked Questions
How accurate is the normal distribution?
The Box-Muller transform produces exact normal distributions. With large sample sizes (>1000), your generated data should closely match theoretical expectations.
Can I generate correlated normal variables?
This tool generates independent samples. For correlated variables, you would need to apply a Cholesky decomposition to the covariance matrix.
What happens when I set bounds?
By default, out-of-bounds values are discarded. If you check "Force bounds", values will be clamped to the boundaries, which may affect the distribution's shape.
Why is my sample mean not exactly μ?
Sample statistics will vary around the population parameters, especially with smaller samples. This is expected behavior in random sampling.
Can I generate non-normal distributions?
This tool specifically generates normal distributions. For other distributions (uniform, exponential, etc.), try our other random number generators.