The normalpdf( Command

Command Summary

Evaluates the normal probability density function at a point.

Command Syntax

normalpdf(x[,μ, σ])

Menu Location


  1. 2ND DISTR to access the distribution menu
  2. ENTER to select normalpdf(.

Calculator Compatibility


Token Size

2 bytes

normalpdf( is the normal (Gaussian) probability density function.

Since the normal distribution is continuous, the value of normalpdf( doesn't represent an actual probability - in fact, one of the only uses for this command is to draw a graph of the normal curve. You could also use it for various calculus purposes, such as finding inflection points.

The command can be used in two ways: normalpdf(x) will evaluate the standard normal p.d.f. (with mean at 0 and a standard deviation of 1) at x, and normalpdf(x,μ,σ) will work for an arbitrary normal curve, with mean μ and standard deviation σ.


For the standard normal distribution, normalpdf(x) is defined as

\begin{align} \operatorname{normalpdf}(x)=\frac1{\sqrt{2\pi\,}} \, e^{-\frac1{2}x^2} \end{align}

For other normal distributions, normalpdf( is defined in terms of the standard distribution:

\begin{align} \operatorname{normalpdf}(x,\mu,\sigma)=\frac{1}{\sigma} \, \operatorname{normalpdf} \left(\frac{x-\mu}{\sigma}\right) \end{align}

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