P-Value Calculator
Turn a test statistic into a p-value. Choose the distribution, enter the statistic and its degrees of freedom.
Learn how to calculate it yourselfEnter your values
Results update as you type.
How to enter your data
Choose Z, T, Chi-square, or F in Distribution and enter one numeric Test statistic. T and chi-square need degrees of freedom in the first df box; F needs numerator df1 and denominator df2. Z does not use the df boxes. Do not paste raw scores or a count table.
p-value
two-tailed
- Significant at 0.05?
- Yes
Convert a z, t, chi-square, or F test statistic into a p-value. Choose the distribution and enter the statistic and any required degrees of freedom. The calculator uses two-sided probabilities for z and t, and upper-tail probabilities for chi-square and F. It does not calculate a statistic from raw observations or count tables.
Calculate it yourself
Example: convert a z statistic of 2 into a two-sided p-value.
Follow this worked example, then repeat the steps with your own numbers.
Look up the cumulative normal probability
Φ(2) ≈ 0.97725In a standard normal table, find the probability to the left of z = 2. Φ is the cumulative distribution function.
Find the upper tail
P(Z ≥ 2) = 1 − 0.97725 = 0.02275Include the equally extreme negative tail
Two-sided p = 2 × 0.02275 = 0.04550This counts both Z ≥ 2 and Z ≤ −2. The result is below a preselected 0.05 threshold.
For t, use the t distribution with the stated degrees of freedom and double one tail. Chi-square and F use only the upper tail; do not double it. Distribution tables give rounded values, while the calculator evaluates them numerically. A p-value is not the probability that the null hypothesis is true.
Check your answer in the calculatorBuilt into PaperSurvey.io
Read the p-value for a survey comparison together with its test, effect size and underlying counts.
Where it is used
- Teachers: A teacher has already calculated a t statistic and its degrees of freedom and wants the corresponding two-sided p-value.
- Small-business owners: A shop analyst converts a chi-square statistic and its degrees of freedom from a categorical comparison into an upper-tail p-value.
- HR staff: An HR analyst has an ANOVA F statistic and numerator and denominator degrees of freedom and checks its p-value.
What a p-value means
The p-value is the probability of seeing a result at least as extreme as yours if there were really no effect. A p-value below 0.05 is the usual threshold for calling a result statistically significant.
When should you use it?
Use this calculator when you already have a test statistic and know its reference distribution under the null hypothesis. Obtain the statistic and degrees of freedom from the appropriate test. Check the distribution, tail convention, and assumptions before interpreting the p-value. Use a specific test calculator if you still have raw data.
What does the result mean?
The result is a p-value, a number from 0 to 1. It tells you how likely you would see a difference this big if there were really no difference at all. A small p-value means the result is unlikely to be chance, so the difference is probably real. A large p-value means the gap could easily be random. The most widely used cut-off is 0.05: below it, results are usually called 'statistically significant'. Above 0.05, treat the difference as unproven.
Mistakes to avoid
Do not type percentages or averages; enter the actual head counts of people. Do not read a small p-value as proof the difference is large or important; it only says the difference is probably not chance. With very few responses, even a real difference can be missed, so gather enough answers first. Do not keep re-testing until you drop below 0.05, as that creates false alarms. And a p-value above 0.05 does not prove the groups are the same, it just means no difference has been shown.
How to use this calculator
- Choose the null-reference distribution: z, t, chi-square, or F.
- Enter the calculated test statistic as one number.
- Enter the required degrees of freedom for t, chi-square, or F. Z ignores the df boxes.
- Read the p-value alongside the effect size and study design. Compare it with a threshold chosen before examining the data; statistical significance does not establish practical importance or causation.
Worked example
Choose Z and enter a test statistic of 2. The calculator returns a two-sided p-value of about 0.0455. Under the standard normal null model, this is the probability of a statistic at least as extreme in either direction. It is not the probability that the null hypothesis is true.
Frequently asked questions
What do I enter in the statistic and degrees-of-freedom boxes?
Enter the calculated test statistic. For t or chi-square, enter its degrees of freedom in the first df box. For F, enter numerator df1 and denominator df2. Z uses no degrees of freedom.
Where do I get these numbers?
Get the test statistic and any degrees of freedom from the test output or an appropriate formula. Raw observations, response counts, and percentages are not test statistics.
What is a p-value in plain words?
It is the chance that the difference you see is just random luck. The smaller it is, the more likely the difference is real.
What p-value counts as good?
There is no single 'good' value, but the common rule is that anything below 0.05 is treated as a real, 'statistically significant' difference.
Does this calculator accept raw observations or a count table?
No. It converts an already calculated statistic to a probability. Use the t-test, chi-square, ANOVA, or another appropriate calculator first if you have raw observations or counts.
Get Started with PaperSurvey.io Software
Start your 14-day free trial now, no credit card required.