Normal Distribution Calculator
Find the cumulative probability that a normally distributed value falls at or below x.
Calculate
Enter your values below.
Result
P(X ≤ x)
0
Formula used
x is converted to a z-score, then the standard normal cumulative distribution function gives the probability of a value at or below it.
Example: x=68, mean=70, std dev=3 → P(X ≤ 68) ≈ 25.25%.
How to use this calculator
- Enter Value (x), Mean, Standard deviation.
- Press Calculate to see your result instantly.
FAQ
Frequently asked questions
What does the result represent?
The probability that a randomly drawn value from this normal distribution is less than or equal to x.
How is this calculated?
x is converted to a z-score, then the cumulative distribution function of the standard normal curve is applied.
What if I want P(X > x) instead?
Subtract the result from 100%.
How accurate is the calculation?
It uses a well-established polynomial approximation of the error function, accurate to about 7 decimal places.