EVERYDAY CLARITY
Normal Probability Density Calculator
Calculate normal density for supplied mean and standard deviation.
Your result
Standardized value
Probability density
Result for the values shown.
Calculations run in your browser.
What to enter
| Input | Meaning and units |
|---|---|
| Observation | Enter observation using the definition in the method and example. |
| Mean | Enter mean using the definition in the method and example. |
| Standard deviation | Enter standard deviation using the definition in the method and example. |
Understanding your result
These outputs describe the probability model and event definitions you entered. A probability is a number from 0 to 1; a probability density is not itself the probability of one exact continuous value.
Common mistakes
- Entering 25 instead of 0.25 for a probability, or assuming events are independent when the model requires that assumption.
- Confusing an exact-count probability with a cumulative probability, or replacement with sampling without replacement.
Check your calculation
- Check a zero/certain-event boundary and the stated support of the distribution against the worked example.
Calculation checks, sources and review limits
What is the normal probability density at this value?
Calculate normal density for supplied mean and standard deviation.
Common uses
- What is the normal probability density at this value
How it works
z = (x - mean) / sd; pdf = exp(0 - z ^ 2 / 2) / (sd * sqrt(2 * 3.141592653589793))
Worked example
Enter Observation: 0 ; Mean: 0 ; Standard deviation: 1 . Results: Standardized value: 0 ; Probability density: 0.3989422804014327 .