Convert a p-value to the corresponding z-score for left-tailed, right-tailed, or two-tailed tests.
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Tail type
Z-Score
A two-tailed test with p = 0.05 corresponds to z = 1.9604. This is not significant at the 0.05 level.
Interpretation
The p-value of 0.05 is above 0.05, suggesting insufficient evidence to reject the null hypothesis at the 5% significance level.
Also in Statistics
Hypothesis Testing
A p-value to z-score calculator converts a probability value into the corresponding z-statistic from the standard normal distribution. This is the inverse of the z-to-p conversion — useful when you know the desired significance level and need the critical z-value, or when converting published p-values back to test statistics for meta-analysis.
Converting a p-value to a z-score uses the inverse of the standard normal CDF, often written as Φ⁻¹(p) or the probit function.
For a two-tailed test with p-value p: z = Φ⁻¹(1 − p/2). For a one-tailed upper test: z = Φ⁻¹(1 − p). Common critical values include z = 1.645 for α = 0.10 (two-tailed) and z = 1.96 for α = 0.05 (two-tailed).
z = Φ⁻¹(1 − p/2)
Two-tailed z-score from p-value.
z = Φ⁻¹(1 − p)
One-tailed (upper) z-score from p-value.
Frequently asked questions
Common reasons include meta-analysis (combining z-scores across studies), determining critical values for custom significance levels, power analysis calculations, and verifying or reproducing statistical results from published research.
Yes, the conversion is mathematically exact — the z-score and p-value are related through the standard normal CDF, which is a one-to-one function. However, if the original p-value was rounded (e.g., "p < 0.05"), the recovered z-score will only be approximate.
Related
These related calculators come from the same leaf category, nearby sibling categories, or the same top-level topic.
Convert a z-score to a one-tailed or two-tailed p-value using the standard normal distribution.
Calculate p-value from a z-score, t-statistic, or chi-square statistic with significance level indicators.
Find critical values for z, t, and chi-square distributions at any significance level and tail type.
Compute count, sum, mean, median, mode, range, variance, and standard deviation from a list of numbers.
