Probability Density Calculator

Calculate the probability density of a normal distribution at a chosen x value, using a mean and standard deviation.

Formula:
f(x) = 1 / (σ√(2π)) × exp(−(x−μ)² / (2σ²))

Result will appear here.
Metric Value

Privacy: calculations run locally in your browser. No inputs are stored or transmitted.

How it works

This page evaluates the normal distribution density at a single x value. A larger density means the x value is more concentrated around the mean for the given standard deviation.

Examples

  • x = 70, μ = 65, σ = 10
  • The result is the normal density at x = 70, not the probability of exactly 70.

FAQ

  • What does this probability density calculator compute?

    It computes the normal distribution probability density f(x) at a given x, using a mean and standard deviation.

  • Is density the same as probability?

    No. A probability density is not the same as a probability at a single point. For continuous distributions, the probability at an exact point is 0, while density describes relative concentration around that point.

  • What formula is used?

    This page uses the normal density formula f(x) = 1 / (σ√(2π)) × exp(−(x−μ)² / (2σ²)).

  • Why must standard deviation be positive?

    Because the normal density formula divides by the standard deviation and uses its square in the denominator.

  • Are calculations stored?

    No. Everything runs locally in your browser.

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