Z Table & Z Score Calculator

Calculate Z scores and look up standard normal probabilities instantly. Free bidirectional Z-table tool with cumulative probability lookup.

What is a Z Score?

A Z score (also called a standard score) tells you how many standard deviations a data point is from the mean of a distribution. It is calculated by subtracting the population mean from the raw score and dividing by the standard deviation.

A positive Z score means the value is above the mean, while a negative Z score means it is below the mean. A Z score of 0 indicates the value equals the mean exactly.

Z scores are widely used in statistics for comparing scores from different distributions, calculating percentiles, and performing hypothesis testing with the standard normal distribution.

Z Score Formula

The standard formula to convert a raw score into a Z score is:

z = (x − μ) / σ

How to Read the Z-Table

The Z-table (standard normal table) shows the cumulative probability P(Z ≤ z) for a given Z value. Follow these steps:

  1. Split your Z value into two parts: the row is z rounded down to one decimal place.
  2. The column is the second decimal place (0.00 to 0.09).
  3. The intersection of the row and column gives the cumulative probability to the left of z.

Worked Example

Find the probability that a standard normal variable is less than 1.96:

z = 1.96 Row: 1.9, Column: 0.06 P(Z < 1.96) = 0.9750 This means 97.5% of values fall below 1.96 standard deviations.

Frequently Asked Questions

Have another question? Let us know.

What does a Z score of 2 mean?

A Z score of 2 means the value is 2 standard deviations above the mean. About 97.7% of values in a standard normal distribution fall below a Z score of 2 (P(Z < 2) ≈ 0.9772).

How do I find the Z score from a probability?

Use the inverse lookup: enter the cumulative probability (e.g. 0.975 for a 95% confidence interval) and the tool returns the corresponding Z value (≈ 1.96). You can also read the Z-table in reverse.

What is the difference between Z score and Z statistic?

A Z score describes where an individual data point falls in a distribution. A Z statistic (test statistic) is used in hypothesis testing to determine how far a sample statistic is from the null hypothesis, in standard error units.

When is a Z table used instead of a T table?

Use the Z distribution when the population standard deviation is known and the sample size is large (n ≥ 30). Use the t-distribution when σ is unknown and the sample is small.

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