How to Find P-Value: Step-by-Step Guide

Updated 6 November 2026 · Standard formula, shown below

This guide walks you through finding a p-value from a test statistic, a core step in hypothesis testing. You will learn the manual calculation methods for the most common tests, how to use statistical tables, and how to verify your results using software. No prior statistical software experience is needed, but you should know your test statistic value, the degrees of freedom (if applicable), and whether your hypothesis is one-tailed or two-tailed.

What You’ll Need

Your calculated test statistic (z-score, t-score, chi-square value, or F-ratio)
The degrees of freedom for your test (if using t, chi-square, or F distributions)
Whether your test is one-tailed (left or right) or two-tailed
A standard normal (z) table, t-table, chi-square table, or F-table (or access to a calculator/software)

Step-by-Step

Identify your test statistic and its distribution. Determine whether you have a z-score (standard normal), t-statistic, chi-square statistic, or F-statistic. This depends on the test you ran. For example, a one-sample proportion test uses a z-score, while a one-sample mean test with unknown population standard deviation uses a t-statistic.
Determine the direction of your alternative hypothesis. If your alternative hypothesis uses “greater than” (>), you need a right-tailed p-value. If it uses “less than” (<), you need a left-tailed p-value. If it uses "not equal to" (≠), you need a two-tailed p-value.
For a z-score (standard normal distribution): Look up the absolute value of your z-score in a standard normal table. The table gives you the area to the left of that z-score. For a left-tailed test, that area is your p-value. For a right-tailed test, subtract that area from 1. For a two-tailed test, double the smaller of the two tail areas (or double the area you found if your z is negative, or double 1 minus the area if your z is positive).
For a t-statistic: Identify your degrees of freedom (df = n – 1 for a one-sample test). Find the row in a t-table matching your df. Find the column whose critical value is closest to your calculated t-statistic (use the absolute value). The column header (e.g., 0.05, 0.025, 0.01) is the one-tailed probability. For a two-tailed test, double that probability. If your t-statistic falls between two columns, your p-value falls between those two probabilities.
For a chi-square statistic: Find the row in a chi-square table matching your degrees of freedom. Locate where your chi-square value falls among the critical values in that row. The column header above that position gives the right-tailed p-value. For a left-tailed test, subtract that p-value from 1. For a two-tailed test, double the smaller tail (this is rarely used for chi-square).
For an F-statistic: You need two degrees of freedom: numerator (df1) and denominator (df2). Find the F-table for your chosen significance level (e.g., 0.05). Locate the column for df1 and the row for df2. The critical value at that intersection is the threshold. If your F-statistic is larger than that critical value, your p-value is smaller than the table’s significance level. To get an exact p-value, you will typically need software or a calculator.
Verify with software (recommended for exact values). In Excel, use NORM.S.DIST(z, TRUE) for z-scores, T.DIST(t, df, TRUE) for left-tailed t, T.DIST.RT(t, df) for right-tailed t, and T.DIST.2T(ABS(t), df) for two-tailed t. For chi-square, use CHISQ.DIST.RT(x, df). In R, use pnorm(z), pt(t, df), pchisq(x, df), and pf(f, df1, df2).
Interpret your p-value. Compare it to your significance level (alpha, usually 0.05). If p-value < alpha, you reject the null hypothesis. If p-value ≥ alpha, you fail to reject the null hypothesis.

Common Mistakes

Using a one-tailed p-value for a two-tailed test. Always double the one-tailed probability for a two-tailed test, unless your software explicitly gives you the two-tailed value.
Mixing up left and right tails. For a right-tailed test with a positive z-score, you must subtract the table area from 1. For a left-tailed test with a negative z-score, the table area is already your p-value.
Forgetting degrees of freedom. Using the wrong df in a t-table or chi-square table changes your p-value substantially. Recheck your sample size and the formula for df.
Using the absolute value incorrectly. For t-tests, always use the absolute value of your t-statistic when looking up the table, but remember that the direction of the tail still matters for interpretation.
Rounding too early. Rounding your test statistic before looking it up can push it across a table boundary. Keep at least three decimal places until the final p-value.

Tips

Always draw a quick sketch of the distribution and shade the tail(s) you are looking for. This prevents direction errors.
When using tables, remember they give areas to the left for z and t. For chi-square and F, they give right-tail critical values, not probabilities directly.
If your p-value is extremely small (e.g., < 0.0001), report it as "p < 0.0001" rather than a string of zeros.
Use software for any non-standard test or when you need an exact p-value, since tables only give ranges.
Keep your significance level in mind before you start. Decide on alpha before computing the p-value to avoid bias.

Troubleshooting

Your p-value seems too small or too large. Recheck the direction of your alternative hypothesis and whether you doubled the tail. Also verify your test statistic calculation itself.
Your t-statistic is not in the table. If your df is not listed, use the next lower df (conservative approach) or interpolate. Most tables list common dfs like 10, 20, 30, 40, 50, 100; use the closest lower one.
Your z-score is above 3.49. Standard normal tables typically stop at 3.49. For higher values, the p-value is less than 0.0002 (one-tailed). Use software for a precise value.
Software gives a different p-value than the table. This is usually due to rounding or using a two-tailed vs. one-tailed function. In Excel, T.DIST.2T requires a positive t-value; if you input a negative one, you get an error.
You are unsure if your test is one- or two-tailed. Look at your original research question. If it asks “is there a difference?” it is two-tailed. If it asks “is it greater than?” or “is it less than?”, it is one-tailed.

Frequently Asked Questions

What exactly does a p-value mean?

A p-value is the probability of observing a test statistic as extreme as, or more extreme than, the one you calculated, assuming the null hypothesis is true. It is not the probability that the null hypothesis is true.

Can a p-value be exactly 0?

No. A p-value is a probability and therefore lies between 0 and 1. In practice, software may report a value like 0.0000001, but it is never exactly zero. You should report it as p < 0.0001.

What is the difference between p-value and alpha?

Alpha (α) is the significance level you choose before running the test, typically 0.05. The p-value is calculated from your data. You reject the null hypothesis when p-value < alpha.

Do I always double the p-value for a two-tailed test?

Yes, for symmetric distributions like the normal and t-distributions, you double the one-tailed p-value. For asymmetric distributions like chi-square and F, the two-tailed concept is rarely used; you typically only look at the right tail.

Can I find a p-value without a table or software?

For a z-score, you can use the empirical rule for rough estimates (e.g., z = 1.96 gives p ≈ 0.05 for two-tailed). For t, chi-square, and F, exact calculation without tables or software is not practical.

Why do different tables give slightly different p-values?

Tables round critical values to a limited number of decimal places. Different publishers may round differently or use slightly different interpolation methods. Differences are typically small and do not change the conclusion unless your p-value is very close to alpha.

Method: the standard formula for this calculation, rounded as each result states. See how the calculators work or report an error.