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z-table (standard normal distribution)

The cumulative standard normal table — plus an exact lookup so you don’t have to interpolate between printed rows. Every value is computed from the same code our statistics engine uses.

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Exact z lookup

Enter any z-score for exact probabilities — no interpolation needed.

Significance level

z-score (optional)

Critical z (two-tailed, α = .05)	1.960
Critical z (one-tailed)	1.645

Common critical z values

Confidence level	α (two-tailed)	z (two-tailed)	z (one-tailed)
80%	.20	1.282	0.842
90%	.10	1.645	1.282
95%	.05	1.960	1.645
98%	.02	2.326	2.054
99%	.01	2.576	2.326
99.9%	.001	3.291	3.090

Standard normal (z) table — cumulative probability Φ(z)

Each cell is the area under the standard normal curve to the LEFT of z = row + column. Example: z = 1.96 → row 1.9, column .06 → .9750.

z	.00	.01	.02	.03	.04	.05	.06	.07	.08	.09
0.0	.5000	.5040	.5080	.5120	.5160	.5199	.5239	.5279	.5319	.5359
0.1	.5398	.5438	.5478	.5517	.5557	.5596	.5636	.5675	.5714	.5753
0.2	.5793	.5832	.5871	.5910	.5948	.5987	.6026	.6064	.6103	.6141
0.3	.6179	.6217	.6255	.6293	.6331	.6368	.6406	.6443	.6480	.6517
0.4	.6554	.6591	.6628	.6664	.6700	.6736	.6772	.6808	.6844	.6879
0.5	.6915	.6950	.6985	.7019	.7054	.7088	.7123	.7157	.7190	.7224
0.6	.7257	.7291	.7324	.7357	.7389	.7422	.7454	.7486	.7517	.7549
0.7	.7580	.7611	.7642	.7673	.7704	.7734	.7764	.7794	.7823	.7852
0.8	.7881	.7910	.7939	.7967	.7995	.8023	.8051	.8078	.8106	.8133
0.9	.8159	.8186	.8212	.8238	.8264	.8289	.8315	.8340	.8365	.8389
1.0	.8413	.8438	.8461	.8485	.8508	.8531	.8554	.8577	.8599	.8621
1.1	.8643	.8665	.8686	.8708	.8729	.8749	.8770	.8790	.8810	.8830
1.2	.8849	.8869	.8888	.8907	.8925	.8944	.8962	.8980	.8997	.9015
1.3	.9032	.9049	.9066	.9082	.9099	.9115	.9131	.9147	.9162	.9177
1.4	.9192	.9207	.9222	.9236	.9251	.9265	.9279	.9292	.9306	.9319
1.5	.9332	.9345	.9357	.9370	.9382	.9394	.9406	.9418	.9429	.9441
1.6	.9452	.9463	.9474	.9484	.9495	.9505	.9515	.9525	.9535	.9545
1.7	.9554	.9564	.9573	.9582	.9591	.9599	.9608	.9616	.9625	.9633
1.8	.9641	.9649	.9656	.9664	.9671	.9678	.9686	.9693	.9699	.9706
1.9	.9713	.9719	.9726	.9732	.9738	.9744	.9750	.9756	.9761	.9767
2.0	.9772	.9778	.9783	.9788	.9793	.9798	.9803	.9808	.9812	.9817
2.1	.9821	.9826	.9830	.9834	.9838	.9842	.9846	.9850	.9854	.9857
2.2	.9861	.9864	.9868	.9871	.9875	.9878	.9881	.9884	.9887	.9890
2.3	.9893	.9896	.9898	.9901	.9904	.9906	.9909	.9911	.9913	.9916
2.4	.9918	.9920	.9922	.9925	.9927	.9929	.9931	.9932	.9934	.9936
2.5	.9938	.9940	.9941	.9943	.9945	.9946	.9948	.9949	.9951	.9952
2.6	.9953	.9955	.9956	.9957	.9959	.9960	.9961	.9962	.9963	.9964
2.7	.9965	.9966	.9967	.9968	.9969	.9970	.9971	.9972	.9973	.9974
2.8	.9974	.9975	.9976	.9977	.9977	.9978	.9979	.9979	.9980	.9981
2.9	.9981	.9982	.9982	.9983	.9984	.9984	.9985	.9985	.9986	.9986
3.0	.9987	.9987	.9987	.9988	.9988	.9989	.9989	.9989	.9990	.9990
3.1	.9990	.9991	.9991	.9991	.9992	.9992	.9992	.9992	.9993	.9993
3.2	.9993	.9993	.9994	.9994	.9994	.9994	.9994	.9995	.9995	.9995
3.3	.9995	.9995	.9995	.9996	.9996	.9996	.9996	.9996	.9996	.9997
3.4	.9997	.9997	.9997	.9997	.9997	.9997	.9997	.9997	.9997	.9998

For negative z, use symmetry: Φ(−z) = 1 − Φ(z). Example: Φ(−1.96) = 1 − .9750 = .0250.

How to read the table

A z-score says how many standard deviations a value sits above (positive) or below (negative) the mean. The table gives Φ(z): the proportion of a standard normal distribution that falls below that z. Find the row for the first two digits (e.g. 1.9) and the column for the second decimal (e.g. .06): Φ(1.96) = .9750, meaning 97.5% of values fall below z = 1.96.

Three standard conversions: the area ABOVE z is 1 − Φ(z); the area between −z and +z is 2Φ(z) − 1; and for a two-tailed p-value, p = 2(1 − Φ(|z|)). That is why z = 1.96 corresponds to the famous 95% interval: 2Φ(1.96) − 1 = .95.

Going the other way (from a probability to a z) is how critical values arise: the z leaving 2.5% in each tail is 1.960, which is where "±1.96 standard errors" in every confidence interval comes from.

Frequently asked questions

What is the z value for 95% confidence?

For a two-sided 95% confidence interval, z = 1.960 (2.5% in each tail). For a one-sided bound at 95%, z = 1.645. For 99%, the two-sided value is 2.576.

How do I look up a negative z-score?

Use symmetry. The normal curve is mirror-imaged around zero, so Φ(−z) = 1 − Φ(z). To find the area below z = −1.28, look up Φ(1.28) = .8997 and subtract: 1 − .8997 = .1003.

When do I use z instead of t?

Use z when the population standard deviation is known or the sample is large (n ≳ 30 the t and z values nearly coincide), and for proportion tests. With a small sample and an estimated SD, use the t-table — its heavier tails compensate for the extra uncertainty.

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