Normal Distribution Calculator (with Graph)
Find normal probabilities and percentiles, with the shaded bell curve.
What the normal distribution calculator does
The normal distribution is the bell-shaped curve that describes many measurements, such as heights, test scores and measurement errors. Enter the mean and standard deviation, choose what you want to find, and the calculator gives the probability and draws the curve with the area shaded. The five tabs cover the questions people ask most:
- Between two values: P(a < X < b).
- Below a value (the left tail), and above a value (the right tail).
- Outside two values: the probability in both tails.
- Value at a percentile: the x that has a given share of the data below it.
Worked examples (IQ scores, mean 100, standard deviation 15)
| Question | Answer |
|---|---|
| P(85 < X < 115), within one standard deviation | 0.6827 (68.27%) |
| P(X ≤ 70), below two standard deviations | 0.0228 (2.28%) |
| P(X ≥ 130), above two standard deviations | 0.0228 (2.28%) |
| P(X < 85 or X > 115) | 0.3173 (31.73%) |
| The 90th percentile | 119.22 |
How it works
The calculator turns each value into a z-score, z = (x − μ) ÷ σ, then reads the probability from the standard normal distribution (the same values as the z-table). For example, 130 is (130 − 100) ÷ 15 = 2 standard deviations above the mean, and about 97.72% of values lie below it. Percentiles go the other way: x = μ + z × σ, where z is the value that leaves your chosen share to its left.
The 68–95–99.7 rule
About 68% of values lie within 1 standard deviation of the mean, 95% within 2 and 99.7% within 3. The bell curve generator draws these bands for any mean and standard deviation.
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.
How to cite this page
CalcPulse. (2026). Normal Distribution Calculator. https://calcpulse.com/normal-distribution-calculator/
Frequently asked questions
How do I calculate a normal probability?
Convert the value to a z-score, z = (x − mean) ÷ standard deviation, then find the area under the standard normal curve. The calculator does both steps.
What is the probability between two values?
It is the area under the curve between them, P(b) − P(a). For a standard normal curve, the area between −1 and 1 is 68.27%.
How do I find a percentile of a normal distribution?
Find the z-score for that percentile, then use x = mean + z × standard deviation. The last tab does this.
What is the difference between the normal distribution and the standard normal distribution?
The standard normal has a mean of 0 and a standard deviation of 1. Any normal distribution can be converted to it with z-scores.
Is my data normally distributed?
Plot a histogram and check that it is roughly symmetric and bell-shaped. Statistical tests such as Shapiro-Wilk can also help.
Last updated