Z-Table (Standard Normal Table)
Cumulative area to the left of z for every z from −3.49 to 3.49. Type a z-score to jump to its cell, or read the table the traditional way.
What the z-table shows
Each cell is the cumulative probability Φ(z): the share of a standard normal distribution lying to the left of z. Because the curve is symmetric, Φ(−z) = 1 − Φ(z), which is why some books print only the positive half.
Values worth memorising
| z = 1.645 | 0.9500 (one-tailed 5%) |
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| z = 1.96 | 0.9750 (two-tailed 5%, 95% CI) |
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| z = 2.326 | 0.9900 (one-tailed 1%) |
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| z = 2.576 | 0.9950 (two-tailed 1%, 99% CI) |
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To go from a raw score to a z first, use the z-score calculator. For areas of any normal distribution without standardising, use the normal distribution calculator.
Frequently asked questions
How do I read a z-table?
Split your z-score into the first decimal and the second. Find the row for the first part (for z = 1.96, the 1.9 row) and the column for the second part (0.06). The cell, 0.9750, is the area under the curve to the left of z.
How do I find the area to the right of z?
Subtract the table value from 1. For z = 1.96, the area to the right is 1 − 0.9750 = 0.0250.
How do I find the area between two z-scores?
Look up both and subtract the smaller from the larger. Between z = −1 and z = 1: 0.8413 − 0.1587 = 0.6826, the “68%” of the empirical rule.
What about negative z-scores?
Use the negative table, or use symmetry: the area left of −z equals the area right of +z. For z = −1.5, the area is 1 − 0.9332 = 0.0668.
What if my z-score is beyond 3.49?
The area to the left is above 0.9998 (or below 0.0002 for negative z). Use the normal distribution calculator for exact tail values far out.