How to use this z-score probability calculator
Enter a z-score above to get the probability (area) below it and above it under the standard normal curve, the two numbers every normal-probability question is built from.
Areas are probabilities
Under the standard normal curve, total area equals 1, so an area is a probability. P(Z < 1.25) = 0.8944 says: a standard normal value falls below 1.25 with probability 0.8944, 89.44% of the time. The same number read as a percentile says the 89th percentile. Three languages, one area.
P(Z > 1.96) = 1 − 0.9750 = 0.025, the 2.5% upper tail that, doubled for both tails, produces the famous 5% significance level. When a paper reports "p < 0.05", this small piece of geometry is what it is standing on.
The three shapes of question
- Below: P(Z < z), read Φ(z) directly.
- Above: P(Z > z) = 1 − Φ(z).
- Between: P(a < Z < b) = Φ(b) − Φ(a). Run the calculator twice and subtract.
Frequently asked questions
How do I find P(Z > z)?
Calculate 1 − Φ(z). The area above a z-score is the complement of the area below it.
What is the probability that Z is between −1 and 1?
Φ(1) − Φ(−1) = 0.8413 − 0.1587 = 0.6827, the empirical rule's 68%.
Is the area below a z-score the same as its percentile?
Yes. Percentile = 100 × area below. A z-score with 0.8944 below it is the 89.44th percentile.