Normal Distribution Visualizer
Explore a normal model locally with adjustable mean, standard deviation, and percentile.
A QUICK WALKTHROUGH
How to use this tool
- Enter the mean and a positive standard deviation.
- Choose a percentile from 0.1% to 99.9% and draw the curve.
- Read the marked value, cumulative probability, and density separately.
Model and formula
Assumes X follows a continuous normal distribution: f(x) = exp(−((x−μ)/σ)²/2) / (σ√(2π)). A percentile is found by numerically inverting an approximate standard normal CDF. No dataset is fitted or checked for normality.
Range and approximation
Mean: −1,000,000 to 1,000,000; standard deviation: 0.001 to 1,000,000; percentile: 0.1% to 99.9%. The graph shows μ ± 4σ and clips the infinite tails. The CDF approximation has absolute error about 1.5 × 10⁻⁷; results are rounded.
GOOD TO KNOW
Common questions
Is curve height a probability?
No. Density can exceed one; probability is area under the curve. The shaded area represents P(X ≤ x), including the left tail beyond the plotted window.
Does this show how my actual data behaves?
Only if a normal model is appropriate. This tool does not estimate parameters, assess normality, or give statistical guarantees.