Bell Curve Generator (Normal Distribution Graph)
Draw a bell curve for any mean and standard deviation, and download the graph.
Draw a bell curve for any mean and standard deviation
Enter a mean (μ) and a standard deviation (σ) and the generator draws the normal curve with the 68–95–99.7 bands shaded and labelled. It also lists the range of values in each band. The default is an IQ-style curve with μ = 100 and σ = 15; try a height curve with μ = 170 and σ = 8 and you get bands of 162 to 178 cm (68.27%), 154 to 186 cm (95.45%) and 146 to 194 cm (99.73%).
Every chart has Download PNG and Download SVG buttons under it, so you can save the image for a report, an essay or a slide. Charts follow your light or dark theme on the page, and the saved image keeps its colours.
What the curve shows
- The curve is highest at the mean, where most values are, and is symmetric on both sides.
- A larger standard deviation makes the curve wider and flatter. A smaller one makes it narrower and taller.
- The total area under the curve is 1 (100%). The shaded bands show how much of that area lies within 1, 2 and 3 standard deviations.
The formula
The height of the curve at x is f(x) = exp(−(x − μ)² ÷ (2σ²)) ÷ (σ × √(2π)). At the mean, the peak height is 1 ÷ (σ × √(2π)), which is about 0.0266 for σ = 15.
To find the probability for a particular range, use the normal distribution calculator. For a histogram of your own data, use the histogram maker.
How to cite this page
CalcPulse. (2026). Bell Curve Generator. https://calcpulse.com/bell-curve-generator/
Frequently asked questions
How do I make a bell curve?
Enter the mean and standard deviation. The generator draws the curve and the bands. You can then download it as a PNG or SVG image.
What is the 68-95-99.7 rule?
In a normal distribution, about 68% of values fall within 1 standard deviation of the mean, 95% within 2 and 99.7% within 3.
What does the standard deviation do to the shape?
A larger standard deviation makes the bell wider and lower, and a smaller one makes it narrower and taller.
Can I use it for my own data?
Yes, if your data are roughly normal. Use your sample's mean and standard deviation. Check the shape with the histogram maker first.
What is the area under a bell curve?
Always 1, or 100%. The area over any range is the probability that a value falls in it.
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