P-Value Calculator: z, t, Chi-Square & F Distributions

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Formula at a glance

P-Value Calculator: z, two-tailed — p = 2·(1 − Φ(|z|)). Example: z = 2.1, two-tailed → p-value: 0.0357288 — How the P-Value Calculator works: z, two-tailed — p = 2·(1 − Φ(|z|))

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📘 About the P

The p-value is the probability of getting a test statistic at least as extreme as yours if the null hypothesis were true. Small p-values (usually below 0.05) count as evidence against the null hypothesis. Every hypothesis test — z, t, chi-square, ANOVA’s F — ends by turning its statistic into a p-value.

Choose the distribution, enter the statistic and degrees of freedom, and pick the tail. The calculator gives the exact p-value (no table lookup), the significance stars used in papers, the decision at your α and the critical values at 10%, 5%, 1% and 0.1%.

🧮 Formula

z, two-tailed

p = 2·(1 − Φ(|z|))

t, two-tailed

p = 2·P(T_df > |t|)

Chi-square / F

p = P(X > statistic)

✏️ Worked examples

z = 2.1, two-tailed

You enter
Distribution	z (standard normal)
Test statistic	2.1
Test	Two-tailed (≠)
Degrees of freedom (t, χ², F numerator)	10
Denominator df (F only)	20
Significance level α	0.05 (95%)

You get
p-value	0.0357288
Significance	* (p < 0.05)
Decision at α = 0.05	Significant at α = 0.05 — reject the null hypothesis (p = 0.0357288 < 0.05)
Distribution · tail	standard normal (z) · two-tailed

p = 0.0357288.

t = 2.5 with 15 df

You enter
Distribution	t (Student)
Test statistic	2.5
Test	Two-tailed (≠)
Degrees of freedom (t, χ², F numerator)	15
Denominator df (F only)	20
Significance level α	0.05 (95%)

You get
p-value	0.0245058
Significance	* (p < 0.05)
Decision at α = 0.05	Significant at α = 0.05 — reject the null hypothesis (p = 0.0245058 < 0.05)
Distribution · tail	t distribution, df = 15 · two-tailed

p = 0.0245058.

🧭 How to use this calculator

What you enter

Distribution
Test statistic
Test
Degrees of freedom (t, χ², F numerator)
Denominator df (F only)
Significance level α

What you get

p-value
Significance
Decision at α = 0.05
Distribution · tail

❓ Frequently asked questions

What p-value is significant?

By convention p < 0.05, but 0.01 or 0.001 are used where false positives are costly. Report the exact p-value.

One-tailed or two-tailed?

Two-tailed unless you decided beforehand to test only one direction. A one-tailed p is half the two-tailed p for z and t.

Is p the probability that the null hypothesis is true?

No. It is the probability of data this extreme assuming the null is true.

p P-Value Calculator (z, t, Chi-Square, F)