About Normal Distribution Bell Curve Explorer & Calculator
Interactive Gaussian normal distribution analyzer and bell curve workbench. Configure mean (μ) and standard deviation (σ), calculate Z-scores, shade custom probability regions (two-tail, between bounds, left tail, right tail), and visualize the 68-95-99.7 Empirical Rule with publication-grade SVG graphics.
Key Capabilities & Features
- Interactive Gaussian bell curve with adjustable population mean (μ) and standard deviation (σ)
- Four flexible area shading modalities: Two-tail (outliers), Between bounds (confidence), Left tail, and Right tail
- Empirical Rule reference benchmarks: 68.27% within ±1σ, 95.45% within ±2σ, and 99.73% within ±3σ
- Accurate Z-score tick mark calibrations along the horizontal baseline
- Exportable high-definition vector SVG graphic ideal for lectures, textbooks, and research papers
How to Use Normal Distribution Bell Curve Explorer & Calculator
Set Mean (μ) & Std Dev (σ)
Enter the center and spread of your continuous normal distribution.
Select Shading Modality
Choose whether to shade between two bounds, one tail, or both tails.
Specify Boundaries a and b
Adjust the lower and upper cutoffs to see the exact probability area.
Inspect the Bell Curve
View the shaded region and verify against the standard empirical rule.
Privacy & In-Browser Execution Guarantee
100% Client-Side. Gaussian probability density calculations and SVG curves render entirely in browser memory.
Frequently Asked Questions
What is the Empirical Rule in statistics?
The Empirical Rule states that for any normal distribution, approximately 68.3% of observations lie within 1 standard deviation of the mean, 95.5% within 2 standard deviations, and 99.7% within 3 standard deviations.
How do you convert any normal value X to a standard Z-score?
Using the transformation formula Z = (X - μ) / σ, which maps any normal distribution to the Standard Normal Distribution N(0, 1).