Standard Normal Distribution Table

Q: How do I read a Z table?

Find the row for the first two digits of your Z score (e.g., 1.9 for Z = 1.96). Then move across to the column matching the hundredths digit (0.06 for Z = 1.96). The intersection gives the cumulative probability: P(Z ≤ 1.96) = 0.9750. This means 97.5% of the standard normal distribution lies to the left of Z = 1.96.

Q: What is the difference between a Z table and an inverse normal calculator?

A Z table lets you look up the probability for a given Z score (forward lookup). An inverse normal calculator does the opposite: you provide a probability and it returns the Z score (reverse lookup). Both use the same underlying cumulative distribution function, just in different directions.

Q: Does the Z table show left tail or right tail probabilities?

The standard Z table (shown on this page) displays left tail cumulative probabilities, meaning P(Z ≤ z). To find the right tail probability, subtract the table value from 1. For example, if the table shows 0.9750 for Z = 1.96, then the right tail probability is 1 - 0.9750 = 0.0250.

Last reviewed: June 2026 by the InvNorm Calculator Editorial Team. Report an issue

The standard normal distribution table, commonly called a Z table, shows the cumulative probability P(Z ≤ z) for Z scores ranging from −3.4 to 3.4. Each cell represents the area under the standard normal curve to the left of the given Z value. This table is essential for statistics courses, hypothesis testing, and confidence interval calculations.

How to Read the Z Table

The table is organized with Z score rows and hundredths-digit columns:

Find the row corresponding to the first decimal place of your Z score. For example, for Z = 1.96, find the row labeled 1.9.
Find the column corresponding to the hundredths digit. For Z = 1.96, find the column labeled 0.06.
Read the value at the intersection. For Z = 1.96, the value is 0.9750. This means P(Z ≤ 1.96) = 0.9750, or 97.50% of the distribution lies to the left.

Reading Tips

For negative Z scores, find the row with the negative value (e.g., −1.9) and use the same column lookup process.
To find a right tail probability, subtract the table value from 1. For Z = 1.96: right tail = 1 − 0.9750 = 0.0250.
To find the probability between two Z values, subtract: P(a < Z < b) = P(Z ≤ b) − P(Z ≤ a).

Complete Z Table: P(Z ≤ z)

This table shows left cumulative probabilities for the standard normal distribution N(0, 1). Use the search box or scroll to find your Z score.

Search for a Z score

Z	0.00	0.01	0.02	0.03	0.04	0.05	0.06	0.07	0.08	0.09
-3.4	0.0003	0.0003	0.0003	0.0003	0.0003	0.0003	0.0003	0.0003	0.0003	0.0002
-3.3	0.0005	0.0005	0.0005	0.0004	0.0004	0.0004	0.0004	0.0004	0.0004	0.0003
-3.2	0.0007	0.0007	0.0006	0.0006	0.0006	0.0006	0.0006	0.0005	0.0005	0.0005
-3.1	0.0010	0.0009	0.0009	0.0009	0.0008	0.0008	0.0008	0.0008	0.0007	0.0007
-3.0	0.0013	0.0013	0.0013	0.0012	0.0012	0.0011	0.0011	0.0011	0.0010	0.0010
-2.9	0.0019	0.0018	0.0018	0.0017	0.0016	0.0016	0.0015	0.0015	0.0014	0.0014
-2.8	0.0026	0.0025	0.0024	0.0023	0.0023	0.0022	0.0021	0.0021	0.0020	0.0019
-2.7	0.0035	0.0034	0.0033	0.0032	0.0031	0.0030	0.0029	0.0028	0.0027	0.0026
-2.6	0.0047	0.0045	0.0044	0.0043	0.0041	0.0040	0.0039	0.0038	0.0037	0.0036
-2.5	0.0062	0.0060	0.0059	0.0057	0.0055	0.0054	0.0052	0.0051	0.0049	0.0048
-2.4	0.0082	0.0080	0.0078	0.0075	0.0073	0.0071	0.0069	0.0068	0.0066	0.0064
-2.3	0.0107	0.0104	0.0102	0.0099	0.0096	0.0094	0.0091	0.0089	0.0087	0.0084
-2.2	0.0139	0.0136	0.0132	0.0129	0.0125	0.0122	0.0119	0.0116	0.0113	0.0110
-2.1	0.0179	0.0174	0.0170	0.0166	0.0162	0.0158	0.0154	0.0150	0.0146	0.0143
-2.0	0.0228	0.0222	0.0217	0.0212	0.0207	0.0202	0.0197	0.0192	0.0188	0.0183
-1.9	0.0287	0.0281	0.0274	0.0268	0.0262	0.0256	0.0250	0.0244	0.0239	0.0233
-1.8	0.0359	0.0351	0.0344	0.0336	0.0329	0.0322	0.0314	0.0307	0.0301	0.0294
-1.7	0.0446	0.0436	0.0427	0.0418	0.0409	0.0401	0.0392	0.0384	0.0375	0.0367
-1.6	0.0548	0.0537	0.0526	0.0516	0.0505	0.0495	0.0485	0.0475	0.0465	0.0455
-1.5	0.0668	0.0655	0.0643	0.0630	0.0618	0.0606	0.0594	0.0582	0.0571	0.0559
-1.4	0.0808	0.0793	0.0778	0.0764	0.0749	0.0735	0.0721	0.0708	0.0694	0.0681
-1.3	0.0968	0.0951	0.0934	0.0918	0.0901	0.0885	0.0869	0.0853	0.0838	0.0823
-1.2	0.1151	0.1131	0.1112	0.1093	0.1075	0.1056	0.1038	0.1020	0.1003	0.0985
-1.1	0.1357	0.1335	0.1314	0.1292	0.1271	0.1251	0.1230	0.1210	0.1190	0.1170
-1.0	0.1587	0.1562	0.1539	0.1515	0.1492	0.1469	0.1446	0.1423	0.1401	0.1379
-0.9	0.1841	0.1814	0.1788	0.1762	0.1736	0.1711	0.1685	0.1660	0.1635	0.1611
-0.8	0.2119	0.2090	0.2061	0.2033	0.2005	0.1977	0.1949	0.1922	0.1894	0.1867
-0.7	0.2420	0.2389	0.2358	0.2327	0.2296	0.2266	0.2236	0.2206	0.2177	0.2148
-0.6	0.2743	0.2709	0.2676	0.2643	0.2611	0.2578	0.2546	0.2514	0.2483	0.2451
-0.5	0.3085	0.3050	0.3015	0.2981	0.2946	0.2912	0.2877	0.2843	0.2810	0.2776
-0.4	0.3446	0.3409	0.3372	0.3336	0.3300	0.3264	0.3228	0.3192	0.3156	0.3121
-0.3	0.3821	0.3783	0.3745	0.3707	0.3669	0.3632	0.3594	0.3557	0.3520	0.3483
-0.2	0.4207	0.4168	0.4129	0.4090	0.4052	0.4013	0.3974	0.3936	0.3897	0.3859
-0.1	0.4602	0.4562	0.4522	0.4483	0.4443	0.4404	0.4364	0.4325	0.4286	0.4247
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

Worked Example: Using the Z Table

Problem: Find P(Z ≤ 2.14) using the table above.

Locate row 2.1 in the Z column.
Move across to column 0.04.
The value is 0.9838.

Therefore, P(Z ≤ 2.14) = 0.9838, meaning about 98.38% of the standard normal distribution lies below Z = 2.14.

Reverse Lookup: Finding Z from Probability

To find the Z score for a given probability, scan the table body for the value closest to your target probability, then read the corresponding row and column headers. For example, to find the Z score for P = 0.9500:

Scan the table for values near 0.9500.
The closest values are 0.9495 (at Z = 1.64) and 0.9505 (at Z = 1.65).
The Z score is approximately 1.645 (interpolating between the two).

For exact reverse lookups, use our InvNorm Calculator or the guide to finding Z scores from probability.

Common Z Values Quick Reference

Z Score	P(Z ≤ z)	Common Use
−2.576	0.0050	99% CI lower critical value
−1.960	0.0250	95% CI lower critical value
−1.645	0.0500	90% CI lower critical value / one-tailed 5%
0.000	0.5000	Median of the distribution
1.645	0.9500	90% CI upper critical value
1.960	0.9750	95% CI upper critical value
2.326	0.9900	One-tailed 1% critical value
2.576	0.9950	99% CI upper critical value

When to Use a Z Table vs. a Calculator

Z tables are useful for quick reference and for understanding the structure of the normal distribution. However, they have limitations:

Tables only cover a finite range of Z scores (typically −3.4 to 3.4).
Precision is limited to four decimal places.
Reverse lookups (probability to Z score) require interpolation.
Tables only work for the standard normal distribution. For custom distributions, you must first convert to Z scores manually.

For higher precision, custom distributions, or reverse lookups, use a calculator such as the InvNorm Calculator, TI-84 invNorm, or Excel NORM.INV.

Frequently Asked Questions

How do I read a Z table?

Find the row for the first two digits of your Z score (e.g., 1.9 for Z = 1.96). Then move across to the column matching the hundredths digit (0.06 for Z = 1.96). The intersection gives the cumulative probability: P(Z ≤ 1.96) = 0.9750. This means 97.5% of the standard normal distribution lies to the left of Z = 1.96.

What is the difference between a Z table and an inverse normal calculator?

A Z table lets you look up the probability for a given Z score (forward lookup). An inverse normal calculator does the opposite: you provide a probability and it returns the Z score (reverse lookup). Both use the same underlying cumulative distribution function, just in different directions.

Does the Z table show left tail or right tail probabilities?

The standard Z table shown on this page displays left tail cumulative probabilities, meaning P(Z ≤ z). To find the right tail probability, subtract the table value from 1. For example, if the table shows 0.9750 for Z = 1.96, then the right tail probability is 1 − 0.9750 = 0.0250.

Standard Normal Distribution Table

How to Read the Z Table

Reading Tips

Complete Z Table: P(Z ≤ z)

Worked Example: Using the Z Table

Reverse Lookup: Finding Z from Probability

Common Z Values Quick Reference

When to Use a Z Table vs. a Calculator

Frequently Asked Questions

Related Calculators

InvNorm Calculator

Z Score from Probability

InvNorm vs NormalCDF

Left vs Right Tail