REFERENCE TABLE · MATH · STATISTICS

Standard Normal Z Table: Cumulative Values to 4 Decimals

The full cumulative normal table from z = 0.00 to 3.49, every cell computed from the normal CDF to 4 decimals: P(Z ≤ 1.96) = 0.9750, P(Z ≤ 1.645) = 0.9500, P(Z ≤ 2.58) = 0.9951. Use the lookup tool for any z — cumulative, upper tail, two-tailed, percentile — or flip it around and get the z for any percentile. Print-friendly.

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Standard normal lookup

Enter a z-score to get the cumulative probability P(Z ≤ z), the upper tail P(Z > z), the two-tailed value, and the percentile — or switch the mode and enter a percentile to get the inverse z. Every figure is computed live from the standard normal CDF; the printed table below matches the same math to 4 decimals. Presets: the classic 1.96, 1.645, and 2.58 cutoffs, plus the 95th and 99th percentile inverses.

Lookup mode

The direction of the lookup. z-score → probabilities reads the table forward (P(Z ≤ z), upper tail, two-tailed, percentile); percentile → z-score inverts it — give it 95 and it returns 1.645.

z-score

Standard deviations from the mean of the standard normal distribution (mean 0, SD 1). 1.96 is the famous one — the two-sided 95% confidence cutoff. Negative z works too: z = −1.96 gives 0.0250 by symmetry.

Percentile

Used in percentile mode: the cumulative percent you want the z-score for. 95 returns 1.645 (the one-sided 95% cutoff), 99 returns 2.326. Must be strictly between 0 and 100.

Result—Enter values above

Enter values to see the result.

The 60-second rule

This table answers one question: how much of the bell curve sits below your z? The standard normal distribution has mean 0 and standard deviation 1; the table lists P(Z ≤ z), the cumulative probability. The cells that run statistics: z = 1.96 → 0.9750 (the two-sided 95% cutoff), z = 1.645 → 0.9500 (one-sided 95%), z = 2.58 → 0.9951 (two-sided 99%), z = 1.28 → 0.8997, z = 0.67 → 0.7486, z = 0.00 → 0.5000. For negative z, use symmetry: P(Z ≤ −z) = 1 − P(Z ≤ z).

The full cumulative Z table (z = 0.00 to 3.49)

Rows are the first decimal of z, columns the second. Find your z’s row and column — the cell is P(Z ≤ z) to 4 decimals. Every cell was computed from the normal CDF (Φ(z) = ½(1 + erf(z/√2))), not transcribed from a printed table, and cross-checked against the standard reference values. Print-friendly — use the print button above the calculator for a clean copy.

z	.00	.01	.02	.03	.04	.05	.06	.07	.08	.09
0.0	0.5000	0.5040	0.5080	0.5120	0.5160	0.5199	0.5239	0.5279	0.5319	0.5359
0.1	0.5398	0.5438	0.5478	0.5517	0.5557	0.5596	0.5636	0.5675	0.5714	0.5753
0.2	0.5793	0.5832	0.5871	0.5910	0.5948	0.5987	0.6026	0.6064	0.6103	0.6141
0.3	0.6179	0.6217	0.6255	0.6293	0.6331	0.6368	0.6406	0.6443	0.6480	0.6517
0.4	0.6554	0.6591	0.6628	0.6664	0.6700	0.6736	0.6772	0.6808	0.6844	0.6879
0.5	0.6915	0.6950	0.6985	0.7019	0.7054	0.7088	0.7123	0.7157	0.7190	0.7224
0.6	0.7257	0.7291	0.7324	0.7357	0.7389	0.7422	0.7454	0.7486	0.7517	0.7549
0.7	0.7580	0.7611	0.7642	0.7673	0.7704	0.7734	0.7764	0.7794	0.7823	0.7852
0.8	0.7881	0.7910	0.7939	0.7967	0.7995	0.8023	0.8051	0.8078	0.8106	0.8133
0.9	0.8159	0.8186	0.8212	0.8238	0.8264	0.8289	0.8315	0.8340	0.8365	0.8389
1.0	0.8413	0.8438	0.8461	0.8485	0.8508	0.8531	0.8554	0.8577	0.8599	0.8621
1.1	0.8643	0.8665	0.8686	0.8708	0.8729	0.8749	0.8770	0.8790	0.8810	0.8830
1.2	0.8849	0.8869	0.8888	0.8907	0.8925	0.8944	0.8962	0.8980	0.8997	0.9015
1.3	0.9032	0.9049	0.9066	0.9082	0.9099	0.9115	0.9131	0.9147	0.9162	0.9177
1.4	0.9192	0.9207	0.9222	0.9236	0.9251	0.9265	0.9279	0.9292	0.9306	0.9319
1.5	0.9332	0.9345	0.9357	0.9370	0.9382	0.9394	0.9406	0.9418	0.9429	0.9441
1.6	0.9452	0.9463	0.9474	0.9484	0.9495	0.9505	0.9515	0.9525	0.9535	0.9545
1.7	0.9554	0.9564	0.9573	0.9582	0.9591	0.9599	0.9608	0.9616	0.9625	0.9633
1.8	0.9641	0.9649	0.9656	0.9664	0.9671	0.9678	0.9686	0.9693	0.9699	0.9706
1.9	0.9713	0.9719	0.9726	0.9732	0.9738	0.9744	0.9750	0.9756	0.9761	0.9767
2.0	0.9772	0.9778	0.9783	0.9788	0.9793	0.9798	0.9803	0.9808	0.9812	0.9817
2.1	0.9821	0.9826	0.9830	0.9834	0.9838	0.9842	0.9846	0.9850	0.9854	0.9857
2.2	0.9861	0.9864	0.9868	0.9871	0.9875	0.9878	0.9881	0.9884	0.9887	0.9890
2.3	0.9893	0.9896	0.9898	0.9901	0.9904	0.9906	0.9909	0.9911	0.9913	0.9916
2.4	0.9918	0.9920	0.9922	0.9925	0.9927	0.9929	0.9931	0.9932	0.9934	0.9936
2.5	0.9938	0.9940	0.9941	0.9943	0.9945	0.9946	0.9948	0.9949	0.9951	0.9952
2.6	0.9953	0.9955	0.9956	0.9957	0.9959	0.9960	0.9961	0.9962	0.9963	0.9964
2.7	0.9965	0.9966	0.9967	0.9968	0.9969	0.9970	0.9971	0.9972	0.9973	0.9974
2.8	0.9974	0.9975	0.9976	0.9977	0.9977	0.9978	0.9979	0.9979	0.9980	0.9981
2.9	0.9981	0.9982	0.9982	0.9983	0.9984	0.9984	0.9985	0.9985	0.9986	0.9986
3.0	0.9987	0.9987	0.9987	0.9988	0.9988	0.9989	0.9989	0.9989	0.9990	0.9990
3.1	0.9990	0.9991	0.9991	0.9991	0.9992	0.9992	0.9992	0.9992	0.9993	0.9993
3.2	0.9993	0.9993	0.9994	0.9994	0.9994	0.9994	0.9994	0.9995	0.9995	0.9995
3.3	0.9995	0.9995	0.9995	0.9996	0.9996	0.9996	0.9996	0.9996	0.9996	0.9997
3.4	0.9997	0.9997	0.9997	0.9997	0.9997	0.9997	0.9997	0.9997	0.9997	0.9998

The worked example, line by line

Setup: z = 1.96, the two-sided 95% confidence cutoff. Question: how much of the curve sits below it?

Line 1 — read the table. Row 1.9, column .06 → 0.9750. So P(Z ≤ 1.96) = 0.9750 — 97.5% of the distribution lies below 1.96.

Line 2 — the upper tail. P(Z > 1.96) = 1 − 0.9750 = 0.0250 — 2.5% sits above it. This is the one-sided p-value for a test statistic of 1.96.

Line 3 — two-tailed. 2 × 0.0250 = 0.0500. The two-sided p-value is 0.05 — exactly why 1.96 is the 95% confidence cutoff: the area between −1.96 and +1.96 is 1 − 0.05 = 95%.

Line 4 — the inverse. Percentile mode: enter 95 → z = 1.645 (P(Z ≤ 1.645) = 0.9500). Enter 99 → z = 2.326. That is the one-sided critical value students confuse with the two-sided 2.58 — the table’s two-sided 99% value is 0.9951 because it leaves 0.5% in each tail.

Output · formula · meaning

Output	Formula	What it means
Cumulative P(Z ≤ z)	Φ(z) = ½(1 + erf(z/√2))	0.9750 for z = 1.96 — the share of the bell curve below your z. The table’s native reading.
Upper tail P(Z > z)	1 − Φ(z)	0.0250 for z = 1.96 — the one-sided p-value of a test statistic, and the tail used for one-sided confidence bounds.
Two-tailed probability	2 × min(Φ(z), 1 − Φ(z))	0.0500 for z = 1.96 — the two-sided p-value. This is the “is it significant at 5%” number.
Percentile	Φ(z) × 100	97.5th percentile for z = 1.96 — the same cumulative probability in percentile language.
Inverse z	z such that Φ(z) = p/100	1.645 for the 95th percentile — the z-score that leaves the given share of the curve below it.

Who uses this

The stats student: looks up 0.9750 at z = 1.96 for the confidence-interval homework, then checks the inverse: the 95th percentile is 1.645, not 1.96 — the classic one-sided vs two-sided mix-up, caught live.
The researcher writing up results: converts a test statistic of 2.58 into a two-tailed p of 0.0099 — significant at 1% — and cites the page in the methods section.
The quality engineer: a process running at z = 3.0 has 0.9987 below it — 1,350 defects per million above it — and sanity-checks the Cpk math against the table.
The data analyst: turns a z-score from a standardized dashboard into a percentile on the fly — z = 0.67 → the 74.9th percentile — for a report that humans can read.

Accuracy & limitations

The table is generated from the normal CDF itself — Φ(z) = ½(1 + erf(z/√2)) — and rounded to 4 decimals, so the maximum rounding error on any cell is ±0.00005. Cross-checks against the standard reference values: 1.96 → 0.9750, 1.645 → 0.9500, 2.58 → 0.9951, 1.28 → 0.8997, 0.67 → 0.7486, 0.00 → 0.5000. The printed table covers z = 0.00 to 3.49; for negative z use the symmetry rule P(Z ≤ −z) = 1 − P(Z ≤ z), and beyond ±3.49 use the lookup tool, which computes the CDF directly. The lookup tool’s erf approximation is accurate to about 10⁻⁷. This table is the standard normal only — for t-distributed statistics with small samples, use a t-table instead.

Cite this calculatorBright Side Kit. “Standard Normal Z Table: Cumulative Values to 4 Decimals | Bright Side Kit.” brightoolbox.com, 2026.

Bright Side Kit. "Standard Normal Z Table: Cumulative Values to 4 Decimals | Bright Side Kit." https://brightoolbox.com/z-table/ Accessed October 24, 2026.

Data sources

Computed, not transcribed — every cell generated from the standard normal CDF, Φ(z) = ½(1 + erf(z/√2)), cross-checked against standard reference values (1.96 → 0.9750; 1.645 → 0.9500; 2.58 → 0.9951; 1.28 → 0.8997; 0.67 → 0.7486; 0.00 → 0.5000).
Abramowitz & Stegun 7.1.26 — the erf approximation used by the lookup tool, accurate to about 10⁻⁷.

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Frequently asked questions

How do you read a z table?

Row plus column gives the cumulative probability. For z = 1.96, find row 1.9 and column .06 — the cell reads 0.9750, meaning P(Z ≤ 1.96) = 0.9750. Split your z into the first decimal (the row) and the second decimal (the column); the intersection is your answer.

What is the difference between one-tailed and two-tailed z values?

The tail count changes which cell you read. Two-tailed 95% confidence uses 1.96 (P ≤ 1.96 = 0.9750, leaving 2.5% in each tail); one-tailed 95% uses 1.645 (P ≤ 1.645 = 0.9500, the whole 5% in one tail). For a p-value, the two-tailed number is double the one-tailed one: 0.0500 vs 0.0250 at z = 1.96.

When do I use a z table vs a t table?

Use the z table when the population standard deviation is known or the sample is large (n ≥ 30); use the t table for small samples with an estimated SD. The t distribution has heavier tails — its critical values are larger than z’s and shrink toward z as the sample grows. With n ≥ 30, the two are close enough that this table works fine.

How do I find negative z values in the table?

Use symmetry — the printed table only goes to 3.49 on the positive side. P(Z ≤ −z) = 1 − P(Z ≤ z), so for z = −1.96 read the 1.96 cell (0.9750) and subtract from 1: 0.0250. The lookup tool at the top computes negative z directly if you’d rather not do the subtraction.

What z value gives 95% confidence?

1.96 for two-sided, 1.645 for one-sided. Two-sided 95% confidence leaves 2.5% in each tail, so you need the z with 0.9750 below it — 1.96. One-sided 95% puts the whole 5% in one tail — 1.645. For 99% the pair is 2.58 (two-sided) and 2.326 (one-sided).

Is the area between −1 and 1 really 68%?

About 68.3%, yes — the 68-95-99.7 rule. P(Z ≤ 1) = 0.8413 and P(Z ≤ −1) = 0.1587; the difference is 0.6826. Between −2 and 2 sits 95.4%, between −3 and 3 sits 99.7% — quick mental math this table turns into exact numbers.

Can I use the table for a non-standard normal distribution?

Yes — standardize first. For any normal X with mean μ and standard deviation σ, compute z = (x − μ) ÷ σ and read this table. The table only knows the standard normal (mean 0, SD 1); the z-score is the translation step that gets you there.