P-value calculator
Compute one-tailed and two-tailed p-values from a z-score.
What this calculator covers
Use this calculator when you already have a z-score and want the corresponding one-tailed and two-tailed tail areas.
This wave focuses on z-based p-values, which keeps the interpretation simple and makes the connection to the normal curve explicit.
Frequently asked questions
- What does a p-value actually measure?
- A p-value is the probability of observing a result at least as extreme as yours, assuming the null hypothesis is true. A small p-value means the data would be unusual if nothing were happening, not that an effect is large or practically important.
- When should I use a one-tailed versus a two-tailed p-value?
- Use a one-tailed p-value when your hypothesis specifies the direction of the effect before seeing the data. Use a two-tailed p-value when you are testing for any difference without a prior directional prediction. Two-tailed tests are the default in most published research.
- Why does this calculator only accept z-scores?
- The tool is scoped to z-based tests, which apply when you have a large enough sample or already know the population standard deviation. For small samples where you would use a t-distribution, a separate t-test calculator is more appropriate.
- What significance threshold should I use?
- Common thresholds are 0.05 and 0.01, but the appropriate cutoff depends on your field and the costs of false positives. A p-value below a threshold indicates statistical significance under that convention, not a universal truth about importance.
Tool
Run the calculation
Result
RESULT · TWO-TAILED P-VALUE
â„–165
Primary result
0.049996
For a z-score of 1.96, the one-tailed p-value in the direction of the statistic is 2.4998% and the two-tailed p-value is 4.9996%.
- Left-tail probability
- 97.5002%
- Right-tail probability
- 2.4998%
- One-tailed p-value
- 2.4998%
- Two-tailed p-value
- 4.9996%
Step-by-step solution
- 1.Treat the entered statistic as a standard normal z-score of 1.96.
- 2.Read the matching tail area from the normal curve: left tail 97.5002% and right tail 2.4998%.
- 3.Use the tail in the direction of the statistic for the one-tailed p-value and double the smaller tail for the two-tailed p-value 4.9996%.
Walkthrough
Visual walkthrough
A p-value from a z-score is just a tail-area lookup on the standard normal curve.
01
Place the statistic on the z-scale
z = 1.96
The z-score tells you how many standard deviations away from the null mean the observed result sits.
02
Read the tail area
97.5002% left · 2.4998% right
The normal CDF gives the cumulative probability to the left, and the complementary probability gives the right tail.
03
Choose one-tailed or two-tailed
One-tailed tests use the tail in the direction of the statistic. Two-tailed tests double the smaller tail to count both extremes.
2.4998% one-tailed · 4.9996% two-tailed