Z Table Calculator

A z table maps a z-score to the area under the standard normal curve — the probability of landing at or below that point. Instead of hunting across rows and columns by hand, this calculator takes a single z-score and instantly returns the cumulative (left-tail) probability, the right-tail probability, and the area between 0 and your z.

How to use this calculator

1. Enter a z-score in the input box (for example, 1.96). A z-score is the number of standard deviations a value sits above or below the mean.
2. Read the cumulative (left-tail) probability — the area under the curve to the left of your z, or the chance of a value at or below it.
3. Read the right-tail probability — the area to the right of your z, which is simply 1 − cumulative.
4. Read the between 0 and z value — the area from the center of the curve out to your z-score, which is the figure a printed table body usually lists.

Worked example

Take a z-score of 1.96, the value behind 95% confidence intervals.

cumulative P(Z < 1.96) = 0.9750   (area to the left)
right-tail  P(Z > 1.96) = 0.0250   = 1 - 0.9750
between 0 and 1.96      = 0.4750   = 0.9750 - 0.5000

So 97.5% of the standard normal curve lies to the left of 1.96, leaving just 2.5% in the right tail. That 2.5% in each tail is exactly why 1.96 marks the cutoff for a 95% confidence interval. For the underlying formulas and conventions, see the NIST/SEMATECH e-Handbook on the normal distribution.

Frequently asked questions

How do I read a z table by hand?

To learn how to read a z table, split your z-score into two parts: the row gives the ones and tenths (for 1.96, the 1.9 row) and the column gives the hundredths (the 0.06 column). The cell where they meet is the probability. This calculator does that lookup for you and shows all three areas at once.

What is the standard normal table?

The standard normal table, also called the z score table, lists probabilities for a normal distribution with a mean of 0 and a standard deviation of 1. Any normal variable can be converted to this scale with a z-score, so one table covers every normal distribution.

Why do some z tables show different numbers?

Some versions of the z score table give the cumulative left-tail area, while others (the “0 to z” style) give only the area from the center out to z. They are two views of the same curve — this tool reports both so you never have to guess which convention a table uses.