Two-tailed z test
z = 1.96p is about 0.0500
P-value Calculator
Use this free p-value calculator to estimate a standard-normal p-value from a z-score, choose left-tailed, right-tailed, or two-tailed mode, and see both tail areas.
Inputs to checkExample numbersCopyable answerTab-only history
Two-tailedp = 0.0499956522
- Left tail
- 0.9750021739
- Right tail
- 0.0249978261
- Z-score
- 1.96
Steps
- Use the standard normal curve where mean is 0 and standard deviation is 1.
- Find the left-tail area for z = 1.96.
- Double the smaller tail area for a two-tailed p-value.
- The p-value is 0.0499956522.
Recent answers
Recent answers will appear here.
Input tips
Two-tailed: Tests difference in either direction.
Right-tailed: Tests unusually high values.
Left-tailed: Tests unusually low values.
How to use the P-value Calculator
- Choose left-tailed, right-tailed, or two-tailed mode.
- Enter the z-score from your statistics problem.
- Press Calculate p-value to see the standard-normal tail areas.
- Use the result as a quick normal-curve estimate, then check whether your assignment needs a different distribution.
What people use it for
Estimate a p-value from a z-score in an introductory statistics example.
Compare left-tailed, right-tailed, and two-tailed z-test choices.
See the left and right standard-normal tail areas before writing an interpretation.
Check a result against a significance level such as 0.05 without claiming proof by itself.
Quick examples
Right-tailed example
z = 1.645right-tail p is about 0.0500
Left-tailed example
z = -1.28left-tail p is about 0.1003
Stronger right-tail result
z = 2.33right-tail p is about 0.0099
No distance from the mean
z = 0, two-tailedp is 1.0000
Strong left-tail result
z = -2.58left-tail p is about 0.0049
Need the guide or a nearby tool?
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- How to use the P-value CalculatorSee slower examples, input meanings, formula notes, result limits, and mistakes to avoid.
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Frequently asked questions
Quick answers about formulas, inputs, examples, result copying, and private in-browser history.
What does this P-value Calculator use?
It estimates p-values from a z-score using the standard normal curve, where the mean is 0 and the standard deviation is 1. It is for z-test style examples, not every statistical test.
Which tail should I choose?
Choose right-tailed when unusually high values support the alternative, left-tailed when unusually low values support it, and two-tailed when unusually high or low values both count as extreme.
What do the main P-value Calculator inputs mean?
Tail type tells the calculator which part of the normal curve counts as extreme. Z-score tells it how many standard deviations your observed result is from the mean.
How should I read the P-value Calculator answer?
Read the p-value as a tail-area estimate for the chosen z-score and tail type. Also check the left-tail and right-tail areas so you can see which side of the curve the result came from.
What does a smaller p-value mean?
A smaller p-value means the observed z-score is farther into the selected tail of the comparison curve. It is evidence to interpret with your study design, assumptions, and chosen significance level, not proof by itself.
Why is the two-tailed value doubled?
A two-tailed test counts extreme results in both directions, so the calculator doubles the smaller tail area and caps the result at 1.
Is this the same as a t-test p-value?
No. A t-test p-value uses a t distribution and degrees of freedom. This calculator uses the standard normal distribution from a z-score.
What should I double-check before trusting the p-value?
Check the z-score sign, the selected tail, and whether your assignment or analysis actually calls for a normal z-test. Use a different calculator or statistics software for t, chi-square, F, exact, or regression p-values.
Does a p-value prove the null hypothesis is false?
No. A p-value describes how unusual the observed z-score would be under the comparison model. It does not measure practical importance, study quality, or the chance that a claim is true.
Is my z-score history private?
Yes. Recent answers stay only in your current browser tab and are not sent to a server.