About P-Value from Z-Score Calculator
This calculator turns a z-score into a p-value for a left, right or two-tailed test, using the standard normal distribution. It is free, needs no sign-up and runs in your browser, so nothing you enter is uploaded.
Use it for a z-test, for a large-sample test of a mean or proportion, or to find how unusual a single standardised value is. The curve shades the rejection region at your significance level and marks the z-score, so you can see at a glance whether it falls inside.
A z-score of 1.96 gives a two-tailed p-value of 0.05, and 1.645 gives a right-tailed p-value of 0.05. The panel under the answer lists both tail areas, so you can read off whichever one the question needs.
How to use P-Value from Z-Score Calculator
- Pick the distribution of your test statistic: z (normal), t, chi-square or F.
- Type the statistic. For t and chi-square add the degrees of freedom, and for F add the numerator and denominator degrees of freedom.
- Choose the alternative hypothesis: two-tailed (not equal), right-tailed (greater than) or left-tailed (less than).
- Choose a significance level, usually 0.05. The critical value and the shaded rejection region follow it.
- Read the p-value and the decision, then open the step-by-step working if you need to show it.
Features
- p-value from a z, t, chi-square or F statistic, left, right or two-tailed.
- Critical value or values for the chosen tail and significance level.
- Left and right tail areas shown separately, so you can check any one-sided claim.
- A bell curve with the rejection region shaded and your statistic marked, readable on a phone.
- Step-by-step KaTeX working and a copy button for the result.
- Non-integer degrees of freedom are accepted, for example the Welch value 17.776.
- A plain-English conclusion that says what the p-value means and what it does not.
P-value from a z-score
With Φ the standard normal cumulative distribution function, the tails are found from the area under the bell curve.
left-tailed p = Φ(z)
right-tailed p = 1 − Φ(z)
two-tailed p = 2 × (1 − Φ(|z|))Worked examples
z = 1.96, two-tailed gives p = 0.05, critical values ±1.96
z = 1.645, right-tailed gives p = 0.04998, critical value 1.645
z = 2.58, two-tailed, α = 0.01 gives p = 0.00988, critical values ±2.576
Privacy: how it works
- The p-values come from distribution functions that run in your browser tab. Nothing you type is sent to Ulkaa or anyone else.
- There is no account, and nothing is stored once you close the tab.
Tips
- Match the tail to the question you asked before you saw the data. Switching to a one-tailed test afterwards to get below 0.05 is not honest.
- Write the p-value with its test and degrees of freedom, for example t(10) = 2.23, p = 0.05, rather than only "significant".
- When software prints "p = 0.000", the true value is just very small. Report p < 0.001 instead.
- Degrees of freedom do not have to be whole numbers. Welch t-tests give fractional degrees of freedom, and you can type them as they are.
Frequently asked questions
Is it really free?
Yes. There is no price, no trial and no credit card. Ulkaa Tool does the work with your own device, so there is no server bill to pass on to you.
Do I need an account?
No. There is no sign-up and no login. Open the page and use it. An Ulkaa account is not needed for anything on this tool.
Does it run in my browser?
Yes. Your numbers are processed by code running in your browser tab, on your own device.
Is my data uploaded?
No. Your numbers are never sent to Ulkaa or to anyone else. You can check this yourself by watching the Network tab in your browser developer tools while you use the tool.
What p-value does a z-score of 1.96 give?
About 0.05 for a two-tailed test, because 2.5% of the normal curve lies beyond 1.96 in each tail. A one-tailed test at z = 1.96 has p of about 0.025.
Can a z-score be negative?
Yes. A negative z means the value is below the mean. For a two-tailed test only its size matters, and for a left-tailed test a negative z gives a small p-value.
More P-Value Calculator pages
- P-Value CalculatorTurn a z, t, chi-square or F statistic into a p-value, see the critical value, and watch the rejection region on the curve.
- P-Value from T-Score CalculatorEnter a t statistic and its degrees of freedom to get the p-value and the critical t value.
- P-Value from Chi-Square CalculatorEnter a chi-square value and its degrees of freedom to get the right-tail p-value.
- P-Value from F-Statistic CalculatorEnter an F statistic and both degrees of freedom to get the p-value and the critical F value.