Gaussian Random Number Generator
Generate normally distributed random numbers
The center of the distribution (average value)
Controls the spread of the distribution
Generated Numbers
About Gaussian Random Number Generator
The Gaussian Random Number Generator creates random numbers that follow a normal distribution (also known as a Gaussian distribution or bell curve). Unlike uniform random numbers where all values in a range have equal probability, Gaussian random numbers cluster around a central value (the mean) with decreasing probability as you move away from the mean.
This tool is particularly useful for scientific simulations, statistical analysis, and any application where you need to model natural phenomena that follow a normal distribution.
How to Use
- Set the mean (μ) - the central value of the distribution
- Set the standard deviation (σ) - controls how spread out the values are
- Choose how many random numbers you want to generate
- Set the number of decimal places for the results
- Toggle whether to show a histogram visualization
- Click "Generate Numbers" to create your random numbers
- View the results and statistics, and use "Copy All" to copy the numbers to your clipboard
Understanding Normal Distributions
A normal distribution has these key properties:
- Mean (μ) - The center of the distribution and the most likely value
- Standard Deviation (σ) - Measures the spread of the distribution
- About 68% of values fall within 1 standard deviation of the mean
- About 95% of values fall within 2 standard deviations of the mean
- About 99.7% of values fall within 3 standard deviations of the mean
The generator uses the Box-Muller transform, a well-established algorithm for generating normally distributed random numbers from uniform random numbers.
Use Cases
- Scientific Research - Model experimental errors and natural variations
- Finance - Simulate stock price movements and risk models
- Quality Control - Generate test data for manufacturing processes
- Machine Learning - Create synthetic datasets for training algorithms
- Statistics Education - Demonstrate central limit theorem and other statistical concepts
Frequently Asked Questions
What's the difference between uniform and Gaussian random numbers?
Uniform random numbers have equal probability across their range (like rolling a fair die), while Gaussian random numbers cluster around a mean value with decreasing probability as you move away from the mean (like measurement errors or heights in a population).
How accurate is this generator?
This generator uses the Box-Muller transform, which produces high-quality normally distributed random numbers. The sample mean and standard deviation shown in the results should be close to your specified values, especially with larger sample sizes.
Can I get negative numbers?
Yes, a normal distribution can include negative numbers. If your mean is close to zero and your standard deviation is large enough, you'll frequently see negative values. If you need only positive values, you can either set a high mean relative to the standard deviation or filter out negative results.
What does the histogram show?
The histogram visualizes the distribution of the generated numbers. The horizontal axis shows the range of values, and the height of each bar represents how many numbers fall within that range. With enough samples, the histogram should approximate a bell curve shape.