Z P-Value from Z-Score Calculator
Convert a z-score into one-sided or two-sided p-values under the standard normal distribution.
📊 Statistics📐 Formula included🧠 Practice questions✓ Free
Please enter valid values.
Formula and Explanation
Convert a z-score into one-sided or two-sided p-values under the standard normal distribution.
| Concept | Formula or rule |
|---|---|
| P-Value from Z-Score Calculator | Two-sided p = 2[1−Φ(|z|)] |
How to Use This Calculator
- Enter the sample, counts, probabilities, or summary statistics requested above.
- Keep paired lists in the same order and separate values with commas.
- Select the correct test direction or sample/population option when available.
- Press Calculate and interpret the result together with the supporting statistics.
Worked Example
Example: For z=1.96, the two-sided p-value is approximately 0.05.
✓ p ≈ 0.0500
Where This Is Used
School & coursework
Check homework, understand formulas, and verify step-by-step statistics exercises.
Research
Explore estimates, uncertainty, distributions, and relationships before using full statistical software.
Business & data analysis
Summarize variation, compare groups, and communicate data-driven findings clearly.
Common Mistakes to Avoid
⚠️
Doubling the wrong tail
Use the tail beyond |z| for a symmetric two-sided test.
Use the tail beyond |z| for a symmetric two-sided test.
⚠️
Choosing tails after seeing results
The alternative hypothesis should be defined before analysis.
The alternative hypothesis should be defined before analysis.
⚠️
Interpreting p as probability the null is true
It is a probability of data at least this extreme under the null model.
It is a probability of data at least this extreme under the null model.
Practice Questions
1. Approximate two-sided p for z=0?
Answer: 1
2. Which p-value is smaller for positive z: upper or lower tail?
Answer: Upper tail.
3. What is Φ(0)?
Answer: 0.5
Frequently Asked Questions
What does a small p-value indicate?▾
The observed statistic is unusual under the null model.
Is p=0.05 a universal boundary?▾
No.
Can p be exactly zero?▾
Mathematically no for finite z; software may round very small values.