Normal Pdf
Calculator
Results
- Probability density
- 0.129517
- Z-score
- 1.5
Statistical results
| Probability density | 0.129517 |
| Z-score | 1.5 |
formula-map diagram
- Probability density
- 0.129517
- Z-score
- 1.5
Statistical relationship
Formula
f(x) = 1 / (σ√(2π)) × e^(−(x − μ)² / (2σ²))= 0.12951759566589
Note
This is a simplified model: it applies the displayed standard formula to the summary values you entered and assumes their underlying conditions (independence, normality, correct sampling) hold. It does not analyse a real data set. Check the assumptions before relying on the result.
More in Statistics and probability
See all →Frequently asked questions
What does the normal probability density function calculate?+
It calculates the height of the bell curve at a specific x-value, given a mean and standard deviation. This height reflects relative likelihood, not a probability itself, since for continuous distributions probability is only meaningful over a range, not at a single point.
Why isn't the output of this calculator a probability?+
For continuous distributions, the probability of hitting any exact single value is technically zero; probability only accumulates over an interval, found by the area under the curve. The PDF value tells you the curve's height at that point, which is useful for comparison and for calculus-based area calculations, not a standalone probability.
What role do the mean and standard deviation play in the shape of the curve?+
The mean shifts the peak of the bell curve left or right, marking its center. The standard deviation controls the width and height of the curve: a smaller standard deviation produces a tall, narrow peak, while a larger one produces a short, wide spread.
Why is the PDF value highest exactly at the mean?+
The normal distribution is symmetric and unimodal, with values most concentrated near the center and progressively rarer further away. That's why the density function reaches its maximum height exactly at x equals the mean, and decreases smoothly in both directions.
How is the PDF different from the cumulative distribution function (CDF)?+
The PDF gives the curve's height at one point, while the CDF gives the total accumulated probability from negative infinity up to that point, i.e., the area under the curve so far. If you need 'what's the probability of being below this value,' you need the CDF, not the PDF.