P-Value Calculator

Calculate the p-value given a z-score, t-score, chi-square score, or an f-value using the calculator below.


Left-tailed p-value:
Right-tailed p-value:
Two-tailed p-value:
Learn how we calculated this below

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How to Find the P-Value

In statistics, a p-value, or probability value, is the probability of obtaining results at least as extreme as the observed results, assuming that the null hypothesis is correct. In other words, it is the probability of getting a result greater than or equal to the sample results.

Put simply, a p-value is the probability that an observation could occur by chance, which indicates the statistical significance of the observation. A small p-value indicates that an outcome is very unlikely.

A p-value lower than 0.05 often indicates that an observation is statistically significant.

P-values are often found using spreadsheet software or by using generated tables such as a z-table. But, you can also find a p-value using a formula.

P-Value Formula

The formula to find a p-value given a cumulative distribution function is:

p-value = cdf(x)

Thus, the p-value is equal to the cumulative distribution function cdf of the observed value x.

This is known as a left-tailed p-value, which is the probability that the value will be less than the sample distribution.

graphic showing a left-tailed p-value for a standard normal distribution

A right-tailed p-value is the probability that the value will be greater than the sample distribution. You can find the right-tailed p-value using a similar formula.

p-value = 1 – cdf(x)

graphic showing a right-tailed p-value for a standard normal distribution

You can find a two-tailed p-value using the following formula:

p-value = 2 × min(cdf(x), 1 – cdf(x))

graphic showing a two-tailed p-value for a standard normal distribution

How to Find the P-Value from a Z-Score

Given a z-score for a standard normal distribution, you can calculate the p-value using the standard normal distribution formula Φ.

p-value = Φ(z-score)

However, an easier way to find the p-value is to look it up using a z-table, which contains the left-tailed p-values for each z score.

You might also be interested in our empirical rule calculator to find the amount of data within one, two, or three standard deviations of the mean.