Z to P-Value Calculator
Convert a z score into one-tailed and two-tailed p-values.
Convert Z Score to P-Value
A p-value is the tail probability associated with a test statistic. This tool calculates the upper-tail probability and the two-tailed probability for a standard normal z score.
Converting a Z Score to a P-Value
A z score tells you how many standard deviations an observation lies from the mean. Converting that z score to a p-value expresses how unusual the result is under the standard normal model.
Z to P-Value Example
A two-tailed z score near 1.96 corresponds to a p-value close to 0.05, a commonly used significance threshold.
Interpretation
Smaller p-values indicate results farther into the tails of the reference distribution. They do not measure effect size or the probability that a hypothesis is true.
Frequently Asked Questions
Does a negative z score matter?
For a two-tailed test, the magnitude is what determines tail extremity.
Is p = 0 possible?
Not exactly in a continuous theoretical distribution, though software may round extremely small values.
Does p below 0.05 prove importance?
No. Practical importance requires context and effect size.
Methodology, Assumptions and Interpretation
Converting z to a p-value requires a tail convention. A two-sided p-value doubles the smaller tail probability for a symmetric standard normal distribution, while one-sided tests use only the prespecified direction.