How to Read a Z-Table: A Step-by-Step Walkthrough
Every semester, a student reads a z-table confidently, gets 0.9099 where the answer should be 0.0901, and loses the marks anyway. The table wasn't the problem. The lookup was.
Reading a z-table is a 3-step move: split the z-score, find the row, find the column. The number where the row and column meet is the proportion of values at or below your z-score. Let's do it slowly, once, and you'll never fumble it again.
What a z-table is (and the one warning that matters)
A z-table lists areas under the standard normal curve. The standard style — the one this guide and our z score table page use — gives the left-tail area: the share of the distribution at or below each z-score.
Warning first, because it bites people: some textbooks print a different table that gives the area between the mean and z. Same grid, different numbers. Before using any printed table, look at the little shaded diagram at its top. If the shading covers everything left of a mark, it's the left-tail style. If shading hugs the center, adjust accordingly. Thirty seconds, saves the whole problem.
The 3 steps, with z = 1.34
Goal: find what proportion of values fall at or below z = 1.34.
Step 1 — Split the z-score into 1.3 and 0.04. The row handles the ones-and-tenths part (1.3). The column handles the hundredths part (0.04). Every lookup starts with this split, and most errors happen right here — students hunt for "1.34" as a single entry and find nothing.
Step 2 — Find row 1.3 on the left edge.
Step 3 — Slide across to column 0.04. The cell reads 0.9099.
So P(Z ≤ 1.34) = 0.9099. In plain words: about 90.99% of values in a normal distribution fall at or below 1.34 standard deviations above the mean — that's the 90.99th percentile. The z score to percentile calculator confirms it instantly, which is a good habit while you're learning: table first, calculator check second.
Negative z-scores: the mirror trick
Many tables print positive values only. Fine — the curve is symmetric, so negative lookups take one extra step:
For z = −1.50: look up +1.50 → 0.9332. Then compute 1 − 0.9332 = 0.0668.
Why does that work? The area below −1.50 equals the area above +1.50 (mirror images), and the area above +1.50 is everything not below it: 1 − 0.9332. So z = −1.50 is the 6.68th percentile. If your table does include negative rows, you'll find 0.0668 printed directly — same answer, same logic.
Areas between two z-scores: subtract, always
"What proportion of values fall between z = −1 and z = +2?" No single cell answers this. You build it:
- P(Z ≤ 2) = 0.9772
- P(Z ≤ −1) = 0.1587 (via the mirror: 1 − 0.8413)
- Subtract: 0.9772 − 0.1587 = 0.8186
About 81.86% of values fall between one SD below and two SD above the mean. Cross-check with the empirical rule: between −1 and +1 alone is 68.27%, and adding the 1-to-2 band on the right (13.59%) gives 81.86%. Two routes, same answer — that's how you know both are right.
Right-tail areas
"Above z = 1.34" is just the complement: 1 − 0.9099 = 0.0901, or 9.01%. Tables give left areas; right areas are always one minus the table value. Forgetting this flip is one of the most common z-score mistakes we see — a probability of 90.99% above a high score should smell wrong immediately.
Going the other direction
Sometimes you have the area and need the z. Then you search the table's body for the probability and read the row and column back out — the reverse lookup covered in our guide to find the z-score from a percentile. And if you haven't computed the z-score yet at all, the z score formula page shows that calculation step by step.
Practice the forward lookup on three values until the split feels automatic: z = 0.80 (0.7881), z = 2.50 (0.9938), z = −0.67 (mirror: 1 − 0.7486 = 0.2514). Then you're done — you can read any standard z-table in the world.
Frequently asked questions
What does the number in a z-table actually mean?
It's the cumulative probability: the proportion of the distribution at or below your z-score — the area under the bell curve to its left. A table value of 0.8413 for z = 1.00 means 84.13% of values fall at or below one standard deviation above the mean.
My z-table only shows positive values. What do I do with a negative z-score?
Use symmetry. Look up the positive version, then subtract from 1. For z = −1.50, the table gives 0.9332 for +1.50, so the answer is 1 − 0.9332 = 0.0668. Many textbooks print only positives because this mirror trick recovers every negative value in one step.
How do I find the area between two z-scores?
Look up both z-scores and subtract the smaller cumulative probability from the larger. Between z = −1 and z = +2: 0.9772 − 0.1587 = 0.8186, so about 81.86% of values fall in that range. Areas under a curve are always found by subtraction, never by a single lookup.
Are all z-tables laid out the same way?
No — and that's a genuine source of errors. The common style used here gives left-tail (cumulative) area. Some tables give area between the mean and z instead, which needs 0.5 added or subtracted. Check the diagram printed at the top of your table before using a single number from it.