0.321972
0.160986
1
0.321972
0.160986
1
This P-Value Calculator turns a Z-score into a p-value using the standard normal distribution. It’s a quick way to understand how extreme your test statistic is under the null hypothesis.
Enter any Z-score (positive or negative). The calculator uses |Z| to compute both the one-tailed p-value (either side) and the two-tailed p-value, which is commonly used when differences in either direction matter.
A p-value is the probability of getting a result at least as extreme as the one observed, assuming the null hypothesis is true. For a Z-score, we use the standard normal cumulative distribution function (CDF), usually written as Φ(z).
Because the standard normal distribution is symmetric, we work with |z|:
This calculator approximates Φ(z) numerically using an error-function approximation and then applies the formulas above.
The one-tailed p-value (either side) represents the probability of seeing a Z-score at least as large as |z| in one tail of the distribution. The two-tailed p-value counts extreme outcomes on both sides (positive and negative) by doubling the one-tail probability.
In practice, many people compare the p-value to a significance level such as 0.05. A smaller p-value suggests your Z-score would be unlikely if the null hypothesis were true — but it does not directly tell you the probability that the null hypothesis is true.
Inputs
Results
A Z-score of 1 is not very far into the tails. Two-tailed p is about 0.3173.
Inputs
Results
A Z-score of 1.96 is a common benchmark because it corresponds to a two-tailed p-value of about 0.05.
Inputs
Results
Because the calculation uses |z|, -1.64 and +1.64 produce the same p-values.
A p-value tells you how likely it is to observe a result at least as extreme as yours if the null hypothesis is true. Smaller p-values mean the result would be less likely under the null.
One-tailed looks for extremeness in one direction (one tail). Two-tailed looks in both directions and is used when “different in either direction” matters.
The standard normal distribution is symmetric. Using |Z| measures distance from zero and makes the tail probability calculation consistent for positive and negative Z-scores.
No. A small p-value suggests your observed Z-score would be unlikely under the null hypothesis, but it doesn’t prove a specific alternative explanation.
Not necessarily. With large sample sizes, even tiny effects can produce small p-values. Effect size and context still matter.
Roboculator Team
The Roboculator Team explains calculations, planning tools, and practical formulas in clear language for real-life situations.
How helpful was this calculator?
5.0/5 (1 rating)
