Normal Distribution Calculator
Area under the normal curve between any two values.
P(-1 ≤ X ≤ 1)
0.682689
68.269% of the distribution
P(X < -1)
0.158655
P(X > 1)
0.158655
z (lower)
-1
z (upper)
1
ShowHide the working
- 1z-scores: -1 and 1
- 2Area = Φ(1) − Φ(-1) = 0.682689
Formula
P(a ≤ X ≤ b) = Φ((b−μ)/σ) − Φ((a−μ)/σ)How it works
The probability that a normally-distributed value falls between two bounds, via the standard normal CDF.
Example
For a standard normal, the area between −1 and 1 is 0.6827 — the familiar 68%.
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About the Normal Distribution Calculator
Area under the normal curve between any two values. It sits in the Statistics section of NWS Calc, a free collection of calculators that run entirely in your browser. There is no signup, no paywall and no tracking — open the page, enter your numbers, get an answer.
Frequently asked questions
- Is the Normal Distribution Calculator free to use?
- Yes. Every calculator on NWS Calc is completely free, with no signup, no usage limits and no ads.
- Does my data leave my device?
- No. The Normal Distribution Calculator runs entirely in your browser using JavaScript. Nothing you type is uploaded, logged or stored on a server.
- Can I use the Normal Distribution Calculator on my phone?
- Yes. The page is fully responsive and works in any modern mobile or desktop browser — there is nothing to install.
- What else is in Statistics?
- Mean, deviation, regression, probability and distributions. You can browse the full Statistics category for related calculators.