# Normal Distribution Plotter Plot a normal-distribution bell curve as SVG with z-score markers, interval or tail-probability shading, and 68/95/99.7 standard-deviation bands. > Canonical page: https://elysiatools.com/en/tools/normal-distribution-plotter - **Category:** Math & Numbers - **Keywords:** normal distribution, bell curve, gaussian, z-score, standard deviation, probability, svg plot, 68 95 99.7 rule ## Overview Renders a Gaussian PDF as an SVG bell curve (x-axis μ ± 4σ). Overlay σ-bands (±1σ ≈ 68.27%, ±2σ ≈ 95.45%, ±3σ ≈ 99.73%) and shade an interval [a,b], a one-sided tail, or mark a z-score with its percentile. Probabilities via erf (A&S 7.1.26, err <1.5e-7); percentile-to-z via Acklam (err <1.15e-9). A plotter/visualizer — for raw calculation use the Normal Distribution Calculator. ## Inputs - **Mean (μ)** (number) - **Standard deviation (σ)** (number) - **Marker mode** (select) - **Marker value(s) (in z or x — see mode)** (text): e.g. 1.96 (or for interval: -1 1) - **Show σ bands (68/95/99.7%)** (checkbox) - **Decimal places** (number) ## When to use - Visualize how a normal distribution changes for a chosen mean and standard deviation. - Show a central interval, such as the standard normal 95% range from z = -1.96 to z = 1.96. - Illustrate one-sided tail probabilities or mark a z-score and its percentile on a bell curve. ## How it works - Enter the mean (μ) and standard deviation (σ), with σ greater than zero. - Choose whether to show standard-deviation bands or mark an interval, upper tail, lower tail, or point. - Enter marker values in the format required by the selected mode, such as "-1.96 1.96" for an interval. - The tool renders the Gaussian probability density as an SVG across the range μ ± 4σ and applies the selected shading or marker. ## Use cases - Statistics lessons that explain z-scores, percentiles, and the 68/95/99.7 rule. - Quality or measurement analysis that needs a visual view of a modeled normal distribution. - Presentations and reports that show confidence intervals or one-sided tail areas. ## Frequently asked questions ### What does the tool output? It outputs an HTML result containing an SVG normal-distribution bell curve. ### What values are required? You must provide a mean (μ) and a positive standard deviation (σ). ### Which marker modes are available? You can show an interval, an upper tail, a lower tail, or a single z-score point. ### What are the standard-deviation bands? They show approximately 68.27% within ±1σ, 95.45% within ±2σ, and 99.73% within ±3σ. ### Is this a probability calculator? 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