P-Value Calculator
Turn a z-test or t-test statistic into an exact p-value, with a shaded distribution chart and a significance decision at your chosen alpha level.
Results from this calculator are estimates provided for general informational purposes only, based on formulas, rates, and standards commonly accepted as of 2026. Figures may differ slightly from other calculators or professional sources due to rounding methods, differing assumptions, or regional regulations, and rules may change over time. Always consult a qualified professional — such as a financial advisor, healthcare provider, or other relevant specialist — before making decisions based on these results.
P-Value
0.0500
Significance Decision (α = 0.05)
Statistically significant
Example
For a two-tailed test with z = 1.96, the p-value is 0.0500. Since 0.0500 is less than your significance level of 0.05, the result is statistically significant — reject the null hypothesis.
Standard normal distribution — shaded area is the p-value
What is a P-Value Calculator?
A p-value measures the strength of evidence against a null hypothesis. Specifically, it's the probability of observing a test statistic at least as extreme as the one you calculated, assuming the null hypothesis is true. A small p-value means your observed result would be unlikely if there were really no effect — which is evidence the effect is real.
This calculator converts a z-test or t-test statistic directly into a p-value for a one-tailed or two-tailed test, and shades the corresponding area under the distribution curve so you can see exactly what that probability represents.
How the P-Value Is Calculated
For a two-tailed test, the p-value is twice the area beyond the absolute value of the test statistic in one tail, since evidence in either direction counts against the null hypothesis:
A left-tailed test uses the area to the left of the statistic, and a right-tailed test uses the area to the right — each testing a specific direction of effect rather than "any difference at all." For a z-test, the area comes from the standard normal distribution; for a t-test, it comes from the Student's t-distribution with your specified degrees of freedom, computed here via the regularized incomplete beta function.
Z-Test vs. T-Test
Use a z-test when the population standard deviation is known or your sample size is large (generally n ≥ 30), since the sampling distribution is well-approximated by the normal distribution. Use a t-test when you're estimating the standard deviation from a smaller sample — the t-distribution has heavier tails than the normal distribution to account for that extra uncertainty, with the tails getting closer to normal as degrees of freedom increase.
What "Statistically Significant" Actually Means
A result is typically called statistically significant if its p-value falls below a pre-chosen significance level (alpha), commonly 0.05. This means: if the null hypothesis were actually true, you'd see a result this extreme (or more extreme) less than 5% of the time by chance alone. A significant result is evidence against the null hypothesis — it is not proof, and it says nothing about the size or real-world importance of the effect.
Common Misinterpretations
A p-value is not the probability that the null hypothesis is true, and it is not the probability that your results happened by chance. It is the probability of the observed data (or more extreme) given that the null hypothesis is true — a subtle but important distinction that trips up even experienced researchers. A p-value also says nothing about effect size: with a large enough sample, even a tiny, practically meaningless effect can produce a very small p-value.
Example — Your Current Inputs
For a two-tailed test with z = 1.96, the p-value is 0.0500. Since 0.0500 is less than your significance level of 0.05, the result is statistically significant — reject the null hypothesis.
Additional Example — Classic z = 1.96
A z-test statistic of 1.96 is the textbook two-tailed critical value for α = 0.05, since the area beyond ±1.96 under the standard normal curve is almost exactly 0.05. A statistic larger than 1.96 in absolute value therefore always produces a two-tailed p-value below 0.05.
About These Parameters
- Test Type
- Whether your test statistic follows a standard normal (z) or Student's t distribution. This is usually determined by which formula you used to compute the statistic itself.
- Test Statistic
- The z-score or t-score computed from your sample — how many standard errors your observed result sits away from the value the null hypothesis assumes.
- Degrees of Freedom
- Only relevant for a t-test. For a one-sample t-test this is sample size minus 1; other t-tests (paired, two-sample) use different formulas for degrees of freedom.
- Tail
- Two-tailed if your hypothesis is simply "there's a difference"; left- or right-tailed if you specifically predicted the direction of that difference before collecting data.
- Significance Level (α)
- The threshold for "statistically significant," chosen before you look at the data. 0.05 is the most common convention, though some fields use stricter thresholds like 0.01.
Frequently Asked Questions
What does p < 0.05 actually mean?
It means that if the null hypothesis were true, you'd see a result this extreme (or more extreme) less than 5% of the time purely by chance. It does not mean there's a 95% chance your hypothesis is correct.
Should I use a one-tailed or two-tailed test?
Use a two-tailed test unless you had a specific directional hypothesis decided before collecting data. Choosing a one-tailed test after seeing which direction the data leans is a form of p-hacking and inflates your false-positive rate.
Why is my t-test p-value different from a z-test with the same statistic?
The t-distribution has heavier tails than the normal distribution, especially at low degrees of freedom, so the same statistic corresponds to a larger p-value under a t-test than under a z-test. As degrees of freedom grow, the two converge.
Does a smaller p-value mean a bigger effect?
No. P-values are driven by both effect size and sample size — a tiny, practically unimportant effect can produce a very small p-value if the sample is large enough. Always look at effect size and confidence intervals alongside the p-value.