Z Score Table

The standard normal table, made clickable: tap any cell to see its probability and percentile. Every entry is the left-tail area P(Z ≤ z) — the cumulative standard normal probability. Free, no signup.

Interactive z-table lookup

Look up a z-score (0.00–3.99)

Look up

Faster: skip the table and use the z score calculator — an instant z table calculator that gives the same probabilities with the bell curve shaded. The table below is generated from the exact normal distribution, so it never has print errors.

How to read a z-table in 3 steps

A z table (also called a standard normal table) converts any z-score into a cumulative probability — no arithmetic required. Here is the exact procedure:

1. Split your z-score into row and column. The row is the ones-and-tenths digit; the column is the hundredths digit. For z = 1.34, the row is 1.3 and the column is .04.
2. Find the cell where row and column meet. That number is the left-tail probability: the share of the normal distribution at or below your z-score. For z = 1.34 the cell reads 0.9099.
3. Multiply by 100 for the percentile. 0.9099 × 100 = the 90.99th percentile. Done — about 91% of values fall at or below a z-score of 1.34.

Try it on the interactive table above: type 1.34 in the lookup box and watch it highlight the exact cell. Once you have done it twice by hand, the logic sticks — and you will understand what the z score to percentile calculator is doing under the hood.

Worked example: z = 1.34

A student asks: "My z-score is 1.34 — what percentile am I in?" Row 1.3, column .04 → the table gives 0.9099. That is the left-tail probability, so the percentile is 0.9099 × 100 = 90.99th percentile. The right-tail probability is 1 − 0.9099 = 0.0901: about a 9% chance of a higher score. Notice how the worked example mirrors the calculator's output — same number, two routes to it.

Negative z-scores in the table

Most printed tables only list positive z-scores — and that is fine, because the normal curve is symmetric. To handle a negative z-score, use the mirror rule: P(Z ≤ −z) = 1 − P(Z ≤ z).

Example: z = −1.50. Look up +1.50 in the table → 0.9332. Then 1 − 0.9332 = 0.0668 → the 6.68th percentile. The interactive table above covers 0.00–3.99; for negatives, look up the positive value and subtract from 1. (Or let the z score calculator handle negatives directly — it accepts them as input.)

Common critical values

The z critical values every statistics student meets, with their table probabilities:

Z-table critical values

Z-score	Table value P(Z ≤ z)	Percentile	Meaning
1.645	0.9500	95.00th	One-tailed 5% cutoff
1.96	0.9750	97.50th	Two-tailed 5% cutoff
2.576	0.9950	99.50th	Two-tailed 1% cutoff

Table vs calculator — when each wins

• Use the table when you are learning the concept, when an exam requires hand lookup, or when you want to double-check a result and understand where it came from.
• Use the calculator for real work: it is faster, it never misreads a row, it handles negative z-scores directly, and it draws the shaded area so you can see which tail your number describes.
• Use both while studying. Look a value up by hand, then verify it with the z-score-to-percentile converter. When the two agree, you actually understand the material — which is the whole point.

What the numbers in the table actually are

Every cell in a standard normal table is a cumulative probability: the total area under the bell curve from the far left up to that z-score. Because the whole area under the curve equals 1, each entry is a number between 0 and 1 — a probability you can read directly.

Three landmarks make the table intuitive. At z = 0 the table reads 0.5000: exactly half the distribution sits below the mean, which is just symmetry doing its job. At z = 1.00 it reads 0.8413: about 84% of values fall within one standard deviation above the mean or anywhere below it. And as z grows, the entries creep toward 1.0000 without ever quite reaching it — at z = 3.99 the table reads 1.0000 only because of rounding; there is always a whisper of area left in the far tail.

This is also why the table pairs so naturally with the z-score-to-percentile converter: both answer "how much area sits left of this z-score?" — the table by lookup, the converter by direct calculation.

Common z-table mistakes

• Reading the wrong row or column. For z = 1.34 the row is 1.3 and the column is .04 — not row 1.4, not column .03. One slip changes 0.9099 into a different number entirely. The lookup box above highlights the exact cell, which is a good way to train your eye.
• Forgetting the negative mirror. A table of positive z-scores cannot directly answer z = −1.50. Apply symmetry: 1 − 0.9332 = 0.0668. Skipping this step is the single most common z-table error.
• Reporting the probability as the answer when the question asked for a percentile. The table gives 0.9099; the percentile is 90.99th. Multiply by 100 — always.
• Using the table on non-normal data. The table's probabilities assume the standard normal curve. If your data is heavily skewed, the lookup is mathematically valid but practically misleading.
• Over-trusting four decimals. Table values are rounded. For z = 1.96 the table says 0.9750; the true value is 0.9750022. Fine for homework, but for published work use the calculator's full precision.

Frequently asked questions

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