P-Value Calculator

Calculate p-value from test statistic and distribution type.

By Konstantin Iakovlev · Updated April 2026 · Source: Khan Academy

p-value

0.0316

Significant (p<0.05)?

Yes

Results

Test Statistic2.1500
p-value0.031555
Significant at 0.05Yes
Significant at 0.01No

Use the P-Value Calculator above to calculate your results. Enter your values and see instant results — all calculations run in your browser.

Disclaimer: This calculator is for informational purposes only and does not constitute tax, financial, or legal advice. Results are estimates based on the information you provide and current rates. Always consult a qualified tax professional or financial advisor for advice specific to your situation.

How It Works

A p-value answers a precise question: if the null hypothesis were true, how likely is a test statistic at least as extreme as the one your sample produced? That single number carries real weight in 2026, where it shapes calls that range from pharmaceutical trials with multi-billion dollar stakes to tuning AI models serving users worldwide. The tool returns that tail probability for the statistic you supply.

Computation relies on the cumulative distribution function tied to whichever distribution fits your test, whether that is the Z-distribution, the t-distribution, or the Chi-squared distribution, and it measures the area in the relevant tail or tails. A two-tailed Z-statistic of 1.96 yields P(Z < -1.96) + P(Z > 1.96), whereas a right-tailed t-test resolves to P(T > t_statistic, df).

Your distribution choice has to match the shape and sample size of your data, because a mismatch quietly distorts the result. Note too what a p-value is not: a value below 0.05 is evidence against the null, not proof that the alternative holds, and the number says nothing about how large the underlying effect actually is.

Example: Evaluating a New Biofuel Catalyst in 2026

  1. 1 Step 1: A research team in 2026 is testing a new biofuel catalyst. They hypothesize it will increase yield. After 100 trials, the average yield increase is 2.5% with a standard deviation of 1.2%. The null hypothesis states no increase. They calculate a Z-statistic of 2.08.
  2. 2 Step 2: Using the standard normal distribution (Z-distribution) for a one-tailed (right-tailed) test, we need to find the probability of observing a Z-score greater than or equal to 2.08. We look up the cumulative probability for Z = 2.08, which is approximately 0.9812.
  3. 3 Step 3: To find the p-value for a right-tailed test, we subtract the cumulative probability from 1: P-value = 1 - 0.9812 = 0.0188.
  4. 4 Step 4: The calculated p-value is 0.0188. If their pre-determined significance level (alpha) was 0.05, then since 0.0188 < 0.05, they would reject the null hypothesis, concluding there is statistically significant evidence that the new biofuel catalyst increases yield.

Source: Khan Academy · Last updated: April 2026

Frequently Asked Questions

What does a p-value actually mean?
A p-value is the probability of obtaining results at least as extreme as the observed results, assuming the null hypothesis is true. A p-value of 0.03 means there is a 3% chance of seeing your data if there were truly no effect.
Is a p-value below 0.05 always significant?
The 0.05 threshold is a convention, not a universal truth. Context matters: medical trials often require 0.01 or lower, while exploratory research may accept 0.10. Also, a small p-value with a tiny effect size may not be practically meaningful.
What is the difference between one-tailed and two-tailed p-values?
A two-tailed test checks for an effect in either direction (greater or less), while a one-tailed test only checks one direction. Two-tailed p-values are twice the one-tailed value. Use two-tailed unless you have a strong prior reason to test only one direction.

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