P-Value Calculator

High-Precision Statistical Significance Calculator with 9 Decimal Places Accuracy

Professional p-value calculator for t-tests, z-tests, F-tests, and chi-square tests • Supports two-tailed, left-tailed, and right-tailed tests

Last updated: November 21, 2025

CreatorFrank Zhao

Test Type

Type of P-Value

Significance Level (α)

Your Z-score

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Overview: what this calculator does

This tool converts a test statistic (like $z$ , $t$ , $\chi^2$ , or $F$ ) into a p-value using the corresponding probability distribution. In plain terms: it answers “How surprising is my statistic if the null hypothesis $H_0$ were true?”

Who is this for?

Students checking homework or lab reports.
Researchers comparing results to a chosen significance level $\alpha$ .
Analysts interpreting outputs from stats software (where you already have the statistic and degrees of freedom).

✅ Important: a p-value is not the probability that $H_0$ is true. It is a probability about the data (or more extreme data) assuming $H_0$ .

If you also want an interval estimate (not just a “significant / not significant” decision), pair this with our Confidence Interval Calculator.

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Quick start: how to use it

Pick the test type

Choose $z$ , $t$ , $\chi^2$ , or $F$ based on your analysis.

Choose the tail

Two-tailed tests look for differences in either direction. One-tailed tests focus on a specific direction.

Set your significance level

Pick $\alpha$ (commonly $0.05$ ) before looking at the result.

Enter your statistic (and degrees of freedom if needed)

For $t$ , $\chi^2$ , and $F$ tests, degrees of freedom matter.

Read the decision

The calculator compares $p$ to $\alpha$ and shows a recommendation (reject or fail to reject $H_0$ ).

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Interpretation tip: treat the p-value as one piece of evidence. If you can, also report an effect size and a confidence interval.

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Worked examples (step-by-step)

Example 1: two-tailed z-test

Suppose you computed $z = 1.96$ and you want a two-tailed p-value.

p

=

2\,(1-\Phi(|z|))

=

2\,(1-\Phi(1.96))

\approx

0.0500

If your chosen threshold is $\alpha = 0.05$ , this is right on the border. In practice, that’s a cue to look at context, effect size, and whether the study is well-powered.

Example 2: two-tailed t-test

Suppose you have $t = 2.14$ with $df = 28$ .

p

=

2\,(1-F_{t,df}(|t|))

=

2\,(1-F_{t,28}(2.14))

\approx

0.041

With $\alpha = 0.05$ , you would typically reject $H_0$ . But “statistically significant” does not automatically mean “important” — always check the practical size of the effect.

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Real-world use cases

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A/B experiments

Convert a reported test statistic into $p$ to check whether a lift is statistically detectable.

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Clinical studies

Compare $p$ against a pre-registered $\alpha$ when evaluating outcomes.

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ANOVA follow-up

If you already have an $F$ statistic and degrees of freedom, compute the corresponding p-value quickly.

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Survey analysis

Use $\chi^2$ p-values to test independence between categorical variables.

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Quality control

Compare variance metrics (often using $F$ or $\chi^2$ tests) to validate process stability.

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When to use (and when not to)

Especially useful when:

You already have a statistic from software output and need the p-value.
You want to sanity-check a reported p-value (typos happen).
You need to compare multiple tail choices consistently.

⚠️ Not a good fit if you only have raw data. This calculator expects the test statistic (and degrees of freedom where relevant). If you only have raw observations, compute the statistic first using appropriate methods.

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Tips & best practices

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Choose the tail before you look. Switching from two-tailed to one-tailed after seeing the data inflates false positives.

Report what matters. Pair $p$ with effect sizes and confidence intervals whenever possible.

Watch out for multiple testing. If you run many tests, some small p-values will appear by chance.

Common mistakes to avoid

Interpreting $p$ as the probability your hypothesis is correct.
Equating “not significant” with “no effect.” It may simply mean low power.
Chasing thresholds (e.g., treating $p=0.049$ and $p=0.051$ as opposites).

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Calculation method (formulas)

The calculator computes p-values using cumulative distribution functions (CDFs). A CDF gives the probability a random variable is less than or equal to a value.

Two-tailed z-test (standard normal)

p = 2\,(1-\Phi(|z|))

where $\Phi(\cdot)$ is the standard normal CDF

Tail options (common forms)

Left-tailed (z): $p = \Phi(z)$
Right-tailed (z): $p = 1-\Phi(z)$
Two-tailed (t): $p = 2\,(1-F_{t,df}(|t|))$
Right-tailed (chi-square): $p = 1 - F_{\chi^2,df}(\chi^2)$
Right-tailed (F): $p = 1 - F_{F,df_1,df_2}(F)$

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Key concepts (quick definitions)

Null hypothesis vs. alternative

$H_0$ is the “no effect / no difference” statement. $H_1$ (or $H_A$ ) is what you are looking for. The p-value is computed under $H_0$ .

Significance level α

$\alpha$ is the pre-chosen cutoff for how much false-positive risk you are willing to accept. Common values are $0.10$ , $0.05$ , and $0.01$ .

Degrees of freedom

Degrees of freedom ( $df$ ) define the shape of the distribution for many tests. For example, a one-sample t-test typically uses $df = n-1$ .

For a chi-square independence test, $df = (r-1)(c-1)$ where $r$ and $c$ are the number of rows and columns.

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Frequently Asked Questions

Is a smaller p-value always “better”?

Not necessarily. A smaller $p$ means the data is less compatible with $H_0$ , but it does not tell you whether the effect is large, important, or replicable.

Practical tip: always pair $p$ with an effect size and a confidence interval.

What does “fail to reject” mean?

It means you don’t have strong enough evidence (under your chosen $\alpha$ ) to reject $H_0$ . It does not prove $H_0$ is true.

Why do large samples often produce tiny p-values?

With enough data, even very small effects can become detectable. That’s why a tiny $p$ can coexist with a trivial practical difference.

Should I use one-tailed or two-tailed?

If you would care about an effect in either direction, use a two-tailed test. Only use a one-tailed test when the opposite direction is truly irrelevant and the direction was justified ahead of time.

Can I compute a p-value without a test statistic?

Not with this tool. You need $z$ , $t$ , $\chi^2$ , or $F$ (and degrees of freedom where required). If you only have raw data, compute the statistic first.

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Limitations & sources

Disclaimer: this calculator is for educational purposes. It does not replace statistical, medical, legal, or financial advice. For high-stakes decisions, consult a qualified professional.