Z Table Calculator
This z table calculator does the whole lookup for you: type a z score and get the area to the left, the area to the right, the area between the mean and z, and the percentile — with the region shaded on the curve. Or work backwards: type a probability and get the z score. A p-value tool and a between-two-scores solver are built in.
P-value from a z statistic
If your z score came from a hypothesis test, the number you actually need is the p-value — the probability of a result at least as extreme as yours if the null hypothesis were true. Pick the test type honestly: it must match the alternative hypothesis you set before looking at the data, not the answer you would prefer afterwards.
Worked check — z = 2.17, two-tailed
The cumulative table gives Φ(2.17) = 0.9850, so one tail beyond 2.17 holds 0.0150. A two-tailed test counts both extremes: p = 2 × 0.0150 = 0.0300, significant at the 0.05 level. Try it in the tool above: enter 2.17, choose two-tailed, and it returns 0.0300. For z = −1.84 in a left-tailed test, p = Φ(−1.84) = 0.0329; the same statistic two-tailed gives 0.0658 — which is why the tail choice is a design decision, not a detail.
What each calculator mode does
- Z score → areas (the finder). Enter any z, positive or negative, to two or more decimal places. Unlike the printed table, the calculator does not round your z to the nearest hundredth first, so 1.645 returns exactly 0.9500 rather than a value interpolated between cells.
- Probability → z score (reverse lookup). Enter a cumulative probability such as 0.975 and the calculator returns z = 1.96. This is how critical values, percentile cutoffs and confidence-interval z values are found. Enter the probability as a decimal, not a percentage.
- Between two z scores. Enter both ends of a range and get the area between them, with the two-step table method printed underneath the answer so you can reproduce it on paper in an exam.
- P-value tool. Converts a test statistic into one-tailed or two-tailed p-values and states the 0.05 significance verdict in plain words.
Calculator or table — which should you use?
Use the calculator to check, and the table to learn and to sit exams. The table teaches the geography of the curve — tails, symmetry, the 0.5 split at the mean — and it is what you will be handed in most exam halls, where calculators like this one are not allowed. The calculator wins on speed, on unrounded inputs (z = 1.645, 2.576), and on reverse lookups, where a printed table forces you to hunt through 800 cells for a value that may fall between two of them. Professionals move between both: table for the method, calculator for the verification. Every number this calculator returns comes from the same cumulative distribution function that generates our tables, spot-checked at the standard anchors (0.00 → 0.5000, 1.96 → 0.9750, 2.576 → 0.9950), so the two can never disagree.
If your starting point is a raw score rather than a z score — a mark, a height, a time — standardise it first with z = (X − μ) / σ. The how to calculate z score page walks through that step with a built-in worked method, and the formula page covers the sample version with x̄ and s.
Frequently asked questions
How accurate is this z table calculator?
It computes the standard normal cumulative distribution directly (the same function statistical software uses), accurate well beyond the four decimal places displayed. Printed tables round every entry to four places; the calculator matches those rounded values at every anchor we test, including 1.96 → 0.9750.
Can the calculator find a z score from a percentile?
Yes — that is the reverse lookup. Convert the percentile to a decimal probability (95th percentile → 0.95), enter it in the probability box, and the calculator returns z = 1.645. For a percentile below the median the answer is negative: the 5th percentile (0.05) returns −1.645.
Why does my calculator answer differ from my textbook table in the last decimal?
Rounding. A printed table stores Φ(1.645) as either 0.9495 (z = 1.64) or 0.9505 (z = 1.65) because it has no 1.645 row; the calculator evaluates 1.645 exactly and returns 0.9500. Near a significance boundary, the calculator's value is the one to trust.
What is the difference between this and a z score calculator?
A z score calculator starts from a raw value, a mean and a standard deviation, and produces a z score. This z table calculator starts from the z score and produces areas, probabilities and percentiles — the step that comes after. Most real problems need both, in that order.
Does the calculator handle negative z scores and two-tailed tests?
Yes to both. Negative z scores return their (small) left-tail areas directly, and the p-value tool's two-tailed mode doubles the correct tail — the one beyond |z| — never the cumulative entry itself.
Prefer the grid? The full z score table is one click away, and how to read a z score table teaches the manual method this calculator automates.