Z table — standard normal distribution

Positive z — area to the left

Negative z — area to the left

The values worth memorising

Questions people actually ask

How do you read a z table?

Find the row for the first two digits of z and the column for the second decimal. z = 1.96 is row 1.9, column 0.06, and the cell is 0.9750 — the area to the left of 1.96. Some European tables print the area between 0 and z instead, so the same z reads 0.4750 there. Both are right; subtract 0.5 to get from this convention to that one.

What does the number in the cell mean?

The probability that a standard normal value falls below that z. 0.9750 at z = 1.96 means 97.5% of the distribution sits to the left and 2.5% to the right. Multiply by 100 to read it as a percentile.

Why is 1.96 the number everyone quotes?

Because it leaves 2.5% in each tail, so ±1.96 encloses 95% of the distribution. Every 95% confidence interval is an estimate plus or minus 1.96 standard errors. The rounder 2 gives 95.4%, which is close enough for a rule of thumb and not for a published interval.

How do I find the area to the right?

Subtract the cell from 1. The area right of z = 1.645 is 1 − 0.9500 = 0.0500, which is why 1.645 is the critical value for a one-tailed test at 5%. For the area between two z values, subtract the smaller cell from the larger.

What about negative z?

The distribution is symmetric, so the area left of −z equals 1 minus the area left of z. The negative table below is that subtraction done for you: −1.96 gives 0.0250, exactly 1 − 0.9750.

When do I use a z table instead of a t table?

Use z when the population standard deviation is known or the sample is large — past about 30 observations the two tables agree to two decimals. Use t when you estimated the standard deviation from the sample, which is nearly always the case with real data. At df = 10 the two-tailed 5% value is 2.228 rather than 1.96, and treating it as 1.96 makes an interval 12% too narrow.

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APA

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"Z Table." Rule Calculator, August 16, 2026, https://rulecalculators.com/z-table.

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Rule Calculator. "Z Table." Rule Calculator. Last reviewed August 16, 2026. https://rulecalculators.com/z-table.

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Sources

• NIST/SEMATECH e-Handbook of Statistical Methods — critical values of the t distribution
• NIST/SEMATECH e-Handbook — cumulative distribution function of the standard normal

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