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))
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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.