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Normal Distribution Calculator

Evaluate the bell curve at any point. Enter a value, the mean, and the standard deviation, and the tool returns the probability density at that value, the cumulative probability of being below it, and the probability of being above it. The density comes from the Gaussian formula, while the cumulative value uses an accurate rational approximation of the normal integral, so results match standard tables to several decimals. The cumulative probability answers questions like what fraction of test takers scored below a given mark, or how likely a measurement falls under a threshold. The tool also shows the z score so you can see how many standard deviations from the mean your value sits. This is the everyday calculator behind quality control, grading curves, and risk models. Everything is computed locally in your browser, so your figures never leave your device.

How to use Normal Distribution Calculator

  1. Enter the value, mean and standard deviation.
  2. Submit to calculate.
  3. Read the density and cumulative probability.

Frequently asked questions

What is the probability density here?

The density is the height of the bell curve at your value, showing how concentrated the distribution is at that point.

What does the cumulative probability give?

It gives the probability that a value falls at or below your input, the area under the curve to the left.

Is this the same as a Gaussian distribution?

Yes. The normal and Gaussian distribution are the same bell-shaped curve defined by a mean and a standard deviation.

What is Normal Distribution Calculator?

Evaluate the bell curve at any point. Enter a value, the mean, and the standard deviation, and the tool returns the probability density at that value, the cumulative probability of being below it, and the probability of being above it.

Is Normal Distribution Calculator free to use?

Yes. Normal Distribution Calculator is completely free, with no sign-up and no usage limits.

Does Normal Distribution Calculator work in a web browser?

Yes. Normal Distribution Calculator runs in any modern web browser. There is nothing to download or install.

Is my data private with Normal Distribution Calculator?

Yes. Normal Distribution Calculator runs entirely on your device in your browser, so nothing you enter is uploaded to a server.