Normal Distribution Calculator (Probability)

Math Tools

Probability below, above or between values on a bell curve

FreePrivateInstant
Mean
Standard deviation
Value x
Second value (for “between”)
Full guide, 6 min readThe bell curve: the 68-95-99.7 rule, z-scores and what “rare” really meansRead the story behind this tool →

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History

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Normal Distribution Calculator (Probability) — at a glance

Work out probabilities on a bell curve.

You enter
Mean 100, SD 15, x 120
Calculate Probability
Result
P(X < x)

How to use it — step by step

Mean, standard deviation and the value x (and an optional second value).

1

Enter your values

Fill in the fields. Default numbers are shown so you can see how it works.

2

Press Calculate Probability

The answer appears at once as large result cards.

3

Copy or share

Copy the result, or share a link that opens with your numbers filled in.

Pro tips

Small things that make the result better.

✦About 68% of values lie within one SD of the mean.
✦Set the second value equal to x to ignore the range.
✦The standard normal has mean 0 and SD 1.

Quick facts

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Frequently Asked Questions

What is the z-score?+

How many standard deviations x is from the mean.

How accurate is it?+

About six decimal places, which is enough for study and work use.

Is my data safe?+

Yes. Everything runs inside your own browser. Your text, files and images are never uploaded to any server.

Is this tool really free?+

Yes — completely free, no signup, no watermark and no usage limit.

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