# P-Value Calculator

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

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## On this page:

## 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*. A left-tailed p-value is the probability that the value will be less than the sample 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)

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

p-value = 2 × min(cdf(x), 1 – cdf(x))

### 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.

## Frequently Asked Questions

### What does the p-value tell you?

The p-value tells you the probability that an observation could occur by chance, which indicates the statistical significance of the observation.

### How do you know when to use p-value?

You use the p-value to see if your data is statistically significant or not.

### What p-value is statistically significant?

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

### What does a p-value of 0.05 mean?

A p-value of 0.05 means that your null hypothesis is true.