Normal Distribution Calculator

Normal Distribution Calculator - Calculate Z-Scores, Probabilities, and Areas

Our Normal Distribution Calculator computes probabilities, percentiles, and areas under the bell curve for normal (Gaussian) distributions, the most important probability distribution in statistics appearing throughout natural and social sciences. The normal distribution is a symmetric, bell-shaped curve described by mean (μ) and standard deviation (σ), with approximately 68% of data within one standard deviation, 95% within two, and 99.7% within three. This comprehensive calculator finds probability for ranges (area under curve), computes z-scores and converts to probabilities, determines percentile values for given probabilities, calculates inverse normal (find x for given probability), handles both standard normal and general normal distributions, and generates probability visualizations showing shaded areas. Critical for statistics students learning probability distributions, researchers performing hypothesis testing, quality control engineers using control charts, psychologists interpreting test scores, finance professionals modeling returns, and anyone analyzing normally-distributed data. The tool demonstrates the central limit theorem's implications and shows why the normal distribution appears so frequently in both natural phenomena and statistical methods.