P-Value Calculator — How to Calculate a P-Value
Two-tailed normal p-value from a z-score via an erfc approximation. Example: z = 1.96 → two-tailed p ≈ 0.05. States standard-normal and two-tail assumptions clearly. Runs in your browser for coursework and quick learning checks.
How it works
Enter a z-score from a standard normal test. The tool reports a two-tailed p-value using an erfc approximation of the normal tail. Assumptions stay visible: standard normal sampling model and both tails. Runs in your browser for coursework and quick checks.
Formula and assumptions
Two-tailed p ≈ erfc(|z| / √2) under a standard normal. Keep these limits in mind:
- Assumes a continuous standard normal z (mean 0, variance 1), not a t, χ², or discrete exact test.
- Two-tailed only on this page — both sides of ±|z| are counted.
- Uses a numerical erfc approximation; results are for learning, not certified statistical software.
- A small p-value does not by itself prove a scientific claim.
Example
Example: z = 1.96 → two-tailed p ≈ erfc(1.96 / √2) ≈ 0.05 (about 0.049996 with this approximation).
When to use it
- Homework: convert a known z to an approximate two-tailed p.
- Quick check after computing z from a mean and SD elsewhere.
- Compare the familiar 1.96 ↔ 0.05 rule of thumb with a numeric output.
Frequently asked questions
Is this one-tailed or two-tailed?
Two-tailed. The reported p covers both sides beyond ±|z| under a standard normal.
What distribution is assumed?
A continuous standard normal for z. It is not a t-test, χ², or exact binomial calculator.
Why is z = 1.96 close to 0.05?
Under a standard normal, |z| ≈ 1.96 is the familiar critical value for a two-tailed 5% test; the page’s erfc approximation returns about 0.05.
Does a small p prove the alternative hypothesis?
No. A p-value is a tail probability under stated assumptions, not automatic proof of a claim.
Related tools
Questions or feedback
Something unclear, broken, or missing? Draft a message below — we read every note about these tools.