Reference Tables
Standard Normal Z-Table
P(Z ≤ z)
Cumulative probability lookup for positive z (0.00-3.49) and negative z (-3.49 to -0.10).
Open Table →Reference tables for the standard normal distribution. The z-table lookup remains useful for homework that explicitly asks students to use the table, for verifying calculator output by hand, and for scanning whole regions of the distribution at once.
Future reference tables (t-distribution, chi-square, F-distribution) will land here when the corresponding distribution calculators are added.
When to use these tables
Use the z-table when a textbook problem explicitly directs you to a table lookup, when you want to scan an entire row to see how probability changes with z, or when verifying a calculator result by hand. The table covers positive z from 0.00 to 3.49 (P(Z ≤ z) form) and negative z from −3.49 to −0.10. The symmetry P(Z ≤ −z) = 1 − P(Z ≤ z) covers the gap.
Frequently Asked Questions
- What does each cell in the z-table represent?
- Each cell is the cumulative probability P(Z ≤ z) under the standard normal — the area under the curve to the left of that z value. Row labels give the first decimal place of z; column labels give the hundredths place. So the cell at row 1.5, column 0.06 is P(Z ≤ 1.56) ≈ 0.9406.
- Why does the negative table stop at −0.10?
- The negative z-table on this page stops at −0.10 because beyond that range the standard normal's symmetry (P(Z ≤ −z) = 1 − P(Z ≤ z)) is easier to read directly off the positive table than from a much larger negative table. For a small negative z, look up the matching positive value and subtract from 1.
- How precise are the tabulated values?
- Tabulated values are rounded to 4 decimal places — the conventional precision for textbook z-tables. The Z-Score Calculator on this site uses Abramowitz & Stegun's approximation internally and is accurate to roughly 1e-7 if you need more precision than the table offers.
- Is this table the same as the one in my textbook?
- Most introductory stats textbooks use the same P(Z ≤ z) form shown here. Some textbooks publish a 'middle area' table (P(0 ≤ Z ≤ z)) instead, where the cell entries are the area between 0 and z rather than the cumulative from −∞. To convert: middle area + 0.5 = cumulative.