Interactive Z Table | Positive and Negative Z

Lookup area (probability) under the normal curve using given a z score and a probability level.  Find probability areas both for positive and negative values. Check out interactive z score negative and z score positive tables. If you prefer to use a calculator instead of positive or negative z score tables use a z score probability calculator. For quick z score calculation use our z score calculator. 

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Negative Z Scores Table

This z-score table shows the area under the standard normal curve to the left of a given negative z-score. Negative z scores in the first column and probability levels in the first row

Z	.00	.01	.02	.03	.04	.05	.06	.07	.08	.09
-3.9	0.00005	0.00005	0.00004	0.00004	0.00004	0.00004	0.00004	0.00004	0.00003	0.00003
-3.8	0.00007	0.00007	0.00007	0.00006	0.00006	0.00006	0.00006	0.00005	0.00005	0.00005
-3.7	0.00011	0.0001	0.0001	0.0001	0.00009	0.00009	0.00008	0.00008	0.00008	0.00008
-3.6	0.00016	0.00015	0.00015	0.00014	0.00014	0.00013	0.00013	0.00012	0.00012	0.00011
-3.5	0.00023	0.00022	0.00022	0.00021	0.0002	0.00019	0.00019	0.00018	0.00017	0.00017
-3.4	0.00034	0.00032	0.00031	0.0003	0.00029	0.00028	0.00027	0.00026	0.00025	0.00024
-3.3	0.00048	0.00047	0.00045	0.00043	0.00042	0.0004	0.00039	0.00038	0.00036	0.00035
-3.2	0.00069	0.00066	0.00064	0.00062	0.0006	0.00058	0.00056	0.00054	0.00052	0.0005
-3.1	0.00097	0.00094	0.0009	0.00087	0.00084	0.00082	0.00079	0.00076	0.00074	0.00071
-3.0	0.00135	0.00131	0.00126	0.00122	0.00118	0.00114	0.00111	0.00107	0.00104	0.001
-2.9	0.00187	0.00181	0.00175	0.00169	0.00164	0.00159	0.00154	0.00149	0.00144	0.00139
-2.8	0.00256	0.00248	0.0024	0.00233	0.00226	0.00219	0.00212	0.00205	0.00199	0.00193
-2.7	0.00347	0.00336	0.00326	0.00317	0.00307	0.00298	0.00289	0.0028	0.00272	0.00264
-2.6	0.00466	0.00453	0.0044	0.00427	0.00415	0.00402	0.00391	0.00379	0.00368	0.00357
-2.5	0.00621	0.00604	0.00587	0.0057	0.00554	0.00539	0.00523	0.00508	0.00494	0.0048
-2.4	0.0082	0.00798	0.00776	0.00755	0.00734	0.00714	0.00695	0.00676	0.00657	0.00639
-2.3	0.01072	0.01044	0.01017	0.0099	0.00964	0.00939	0.00914	0.00889	0.00866	0.00842
-2.2	0.0139	0.01355	0.01321	0.01287	0.01255	0.01222	0.01191	0.0116	0.0113	0.01101
-2.1	0.01786	0.01743	0.017	0.01659	0.01618	0.01578	0.01539	0.015	0.01463	0.01426
-2.0	0.02275	0.02222	0.02169	0.02118	0.02068	0.02018	0.0197	0.01923	0.01876	0.01831
-1.9	0.02872	0.02807	0.02743	0.0268	0.02619	0.02559	0.025	0.02442	0.02385	0.0233
-1.8	0.03593	0.03515	0.03438	0.03362	0.03288	0.03216	0.03144	0.03074	0.03005	0.02938
-1.7	0.04457	0.04363	0.04272	0.04182	0.04093	0.04006	0.0392	0.03836	0.03754	0.03673
-1.6	0.0548	0.0537	0.05262	0.05155	0.0505	0.04947	0.04846	0.04746	0.04648	0.04551
-1.5	0.06681	0.06552	0.06426	0.06301	0.06178	0.06057	0.05938	0.05821	0.05705	0.05592
-1.4	0.08076	0.07927	0.0778	0.07636	0.07493	0.07353	0.07215	0.07078	0.06944	0.06811
-1.3	0.0968	0.0951	0.09342	0.09176	0.09012	0.08851	0.08691	0.08534	0.08379	0.08226
-1.2	0.11507	0.11314	0.11123	0.10935	0.10749	0.10565	0.10383	0.10204	0.10027	0.09853
-1.1	0.13567	0.1335	0.13136	0.12924	0.12714	0.12507	0.12302	0.121	0.119	0.11702
-1.0	0.15866	0.15625	0.15386	0.15151	0.14917	0.14686	0.14457	0.14231	0.14007	0.13786
-0.9	0.18406	0.18141	0.17879	0.17619	0.17361	0.17106	0.16853	0.16602	0.16354	0.16109
-0.8	0.21186	0.20897	0.20611	0.20327	0.20045	0.19766	0.19489	0.19215	0.18943	0.18673
-0.7	0.24196	0.23885	0.23576	0.2327	0.22965	0.22663	0.22363	0.22065	0.2177	0.21476
-0.6	0.27425	0.27093	0.26763	0.26435	0.26109	0.25785	0.25463	0.25143	0.24825	0.2451
-0.5	0.30854	0.30503	0.30153	0.29806	0.2946	0.29116	0.28774	0.28434	0.28096	0.2776
-0.4	0.34458	0.3409	0.33724	0.3336	0.32997	0.32636	0.32276	0.31918	0.31561	0.31207
-0.3	0.38209	0.37828	0.37448	0.3707	0.36693	0.36317	0.35942	0.35569	0.35197	0.34827
-0.2	0.42074	0.41683	0.41294	0.40905	0.40517	0.40129	0.39743	0.39358	0.38974	0.38591
-0.1	0.46017	0.4562	0.45224	0.44828	0.44433	0.44038	0.43644	0.43251	0.42858	0.42465
-0.0	0.5	0.49601	0.49202	0.48803	0.48405	0.48006	0.47608	0.4721	0.46812	0.46414

The Z-table, also known as the Standard Normal Distribution Table, is a mathematical tool used to calculate the probabilities of a standard normal distribution. A standard normal distribution is a normal distribution with a mean of 0 and a standard deviation of 1. The table is used to find the area under the curve to the left or right of a given Z-score, which represents the number of standard deviations from the mean.

There are two Z-tables: the positive Z-table and the negative Z-table. The positive Z-table is used to find the probability of the area under the curve to the right of a given positive Z-score. The negative Z-table, on the other hand, is used to find the probability of the area under the curve to the left of a given negative Z-score.

Here are the steps to use the Z-table:

1. Identify the Z-score you want to find the probability for. The Z-score is the number of standard deviations away from the mean.
2. Determine whether you are looking for the probability to the left or right of the Z-score. If you are looking for the probability of a Z-score of 1.5 or higher, you are looking for the area to the right of the Z-score. If you are looking for the probability of a Z-score of -1.5 or lower, you are looking for the area to the left of the Z-score.
3. Use the positive Z-table for positive Z-scores and the negative Z-table for negative Z-scores.
4. Find the appropriate row and column for your Z-score. If your Z-score is positive, look it up in the positive Z-table. If it is negative, look up the absolute value of the negative Z-score in the positive Z-table.
5. Find the intersection of the row and column that correspond to your Z-score. The value you find is the probability of the area under the curve up to that Z-score.
6. If you are looking for the probability to the left of the Z-score, your answer is the value you found in step 5. If you are looking for the probability to the right of the Z-score, subtract the value you found in step 5 from 1.

Let's look at some examples to clarify the steps:

Example 1:
Suppose you want to find the probability of a Z-score of 1.5 or higher.
Step 1: Identify the Z-score as 1.5.
Step 2: You are looking for the probability to the right of the Z-score.
Step 3: Use the positive Z-table.
Step 4: Find the intersection of the row for 1.5 and the column for 0.00. The value is 0.0668.
Step 5: Subtract the value in step 4 from 1. The probability of a Z-score of 1.5 or higher is 1 - 0.0668 = 0.9332.

Example 2:
Suppose you want to find the probability of a Z-score of -2.25 or lower.
Step 1: Identify the Z-score as -2.25.
Step 2: You are looking for the probability to the left of the Z-score.
Step 3: Use the negative Z-table.
Step 4: Find the intersection of the row for 2.2 and the column for 0.05. The value is 0.0122.
Step 5: The probability of a Z-score of -2.25 or lower is 0.0122.
​
Example 3:
Suppose you want to find the probability of a Z-score of -1

Step 1: Identify the Z-score as -1.
Step 2: You are looking for the probability to the left of the Z-score.
Step 3: Use the positive Z-table and look up the absolute value of -1, which is 1.
Step 4: Find the intersection of the row for 1 and the column for 0.00. The value is 0.1587.
Step 5: The probability of a Z-score of -1 or lower is 0.1587.

In this case, we used the positive Z-table to find the probability to the right of the absolute value of the negative Z-score, and then subtracted the result from 1 to find the probability to the left of the negative Z-score.