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P-Value Calculator

Convert between a Z-score and left-tail, right-tail, center, symmetric interval, or two-tailed normal probabilities.

ExampleSample values — edit any field to see your result.

Enter exactly one value and leave the other fields blank.

Enter exactly one value and leave the other fields blank.

Enter exactly one value and leave the other fields blank.

Enter exactly one value and leave the other fields blank.

Enter exactly one value and leave the other fields blank.

Enter exactly one value and leave the other fields blank.

Results update as you type.

Result

Given Z = 2, Z = 2

Estimated result

Z-score
2
P(x < Z)
0.97725
P(x > Z)
0.022750
P(0 < x < Z)
0.47725
P(−Z < x < Z)
0.95450
P(x < −Z or x > Z)
0.045500
ResultGiven Z = 2, Z = 2

Convert a standard-normal Z-score into one-sided or two-sided probability areas, or work backward from any one area to Z. Enter exactly one field at a time; all other normal-curve probabilities are calculated together.

Formula

If Φ is the standard normal cumulative distribution function:

left tail  = Φ(Z)
right tail = 1 − Φ(Z)
two tails  = 2 × (1 − Φ(|Z|))
between    = 2 × Φ(|Z|) − 1

When a probability is supplied, the calculator uses the inverse normal CDF to find the corresponding Z-score.

Examples

Z-score of 2

For Z = 2, P(x &lt; Z) is 0.97725, the right-tail probability is 0.022750, and the combined two-tail probability is 0.045500.

Frequently asked questions

What probability areas can this calculator convert?
It handles left-tail, right-tail, zero-to-Z center area, the symmetric area between minus Z and Z, and the combined two-tail area.
What is the two-tailed p-value for Z equals 2?
It is approximately 0.045500. Each tail is approximately 0.022750.
Can I calculate a Z-score from a probability?
Yes. Clear the default Z-score, enter exactly one probability field, and the inverse standard normal distribution is used to recover Z.
Is a p-value the probability that the null hypothesis is true?
No. It is the probability, under the null model, of obtaining a result at least as extreme as the observed result according to the selected tail definition.

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