Z-table (standard normal table)

Q: Why do I need both a negative and a positive z-table?

The negative table covers z-scores below the mean (areas less than 0.5) and the positive table covers z-scores above it. Some textbooks print only the positive half and rely on symmetry: the area to the left of −z equals the area to the right of +z.

Q: What if my z-score has more than two decimal places or is beyond ±3.49?

Round to two decimals for the table, or use the lookup above, which calculates the exact area for any z. Beyond about ±3.5 the area is so close to 0 or 1 that tables stop; the lookup still gives the exact value, for example 0.99977 for z = 3.5.

Find the area under the normal curve for any z-score: look it up in the table below, or let the lookup find it and explain each step.

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1 Enter your data
2 Choose an option
3 Click “Look up”
4 Read the result

Negative z-scores (area to the left)

z	.00	.01	.02	.03	.04	.05	.06	.07	.08	.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	0.4960	0.4920	0.4880	0.4840	0.4801	0.4761	0.4721	0.4681	0.4641

Positive z-scores (area to the left)

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

Each value is Φ(z), the area under the standard normal curve to the left of z. Values are rounded to four decimal places.

How to use the z-table

Round your z-score to two decimal places, for example 1.53.
Pick the table: negative for z below 0, positive for z above 0.
Find the row for the ones digit and first decimal (1.5), then the column for the second decimal (.03).
Read the value where they meet: 0.9370. That's the area to the left of z.
For the area to the right, subtract it from 1. Or type your z into the lookup above, choose the area you need, and it will highlight the cell and do the arithmetic.

What the z-table shows

A z-table lists the cumulative probabilities of the standard normal distribution, the bell curve with mean 0 and standard deviation 1. For any z, the value in the table is

Φ(z) = P(Z ≤ z)

and the common variations follow from it:

P(Z > z) = 1 − Φ(z) P(a < Z < b) = Φ(b) − Φ(a)

z: The z-score: how many standard deviations a value is from the mean, z = (x − μ) / σ
Z: A standard normal random variable
Φ(z): The area to the left of z, which is the number printed in the table

To use the table with real data, first convert your value to a z-score with the z-score calculator.

Worked example

SAT math scores are roughly normal with mean 520 and standard deviation 115. What share of students score above 700?

Convert 700 to a z-score
z = (700 − 520) / 115 = 1.565 ≈ 1.57
Positive table, row 1.5, column .07
Φ(1.57) = 0.9418
"Above" means the area to the right
P(Z > 1.57) = 1 − 0.9418 = 0.0582

What it means: about 5.8% of students score above 700. In other words, a 700 is roughly at the 94th percentile.

Tips for reading z-table values

Check the sign first. A negative z always gives an area below 0.5; a positive z gives an area above 0.5.
Remember the landmarks: Φ(0) = 0.5, Φ(1) ≈ 0.8413, Φ(1.645) ≈ 0.95, Φ(1.96) ≈ 0.975 and Φ(2.576) ≈ 0.995. These are the z-values behind 90%, 95% and 99% confidence intervals.
Two-tailed problems need both tails: double the area beyond |z|. For |z| = 1.96, that is 2 × 0.025 = 0.05.
Use the t-table instead when you estimate the standard deviation from a small sample. See the t-table.

Frequently asked questions

How do you read a z-table?

Split your z-score into two parts: the first decimal place and the second. Find the row for the first part (for z = 1.53, the 1.5 row), then move across to the column for the second decimal (.03). The number where they meet, 0.9370, is the area under the standard normal curve to the left of z.

What does the value in a z-table mean?

Each value is a cumulative probability: the proportion of a standard normal distribution that lies below that z-score. 0.9370 for z = 1.53 means 93.70% of values fall below it, so it is the 93.7th percentile. It is also the probability that a randomly chosen value is less than z.

How do I find the area to the right of a z-score?

Subtract the table value from 1. For z = 1.53, the area to the left is 0.9370, so the area to the right is 1 − 0.9370 = 0.0630. Because the curve is symmetric, it is also the table value for −1.53.

How do I find the area between two z-scores?

Look up both and subtract the smaller from the larger. For −1 < z < 1, that is 0.8413 − 0.1587 = 0.6826, the 68% in the empirical rule. The normal distribution calculator does this directly in your own units.

Why do I need both a negative and a positive z-table?

The negative table covers z-scores below the mean (areas less than 0.5) and the positive table covers z-scores above it. Some textbooks print only the positive half and rely on symmetry: the area to the left of −z equals the area to the right of +z.

What if my z-score has more than two decimal places or is beyond ±3.49?

Round to two decimals for the table, or use the lookup above, which calculates the exact area for any z. Beyond about ±3.5 the area is so close to 0 or 1 that tables stop; the lookup still gives the exact value, for example 0.99977 for z = 3.5.

Last reviewed November 11, 2026

Negative z-scores (area to the left)

Positive z-scores (area to the left)

How to use the z-table

What the z-table shows

Worked example

Tips for reading z-table values

Frequently asked questions

How do you read a z-table?

What does the value in a z-table mean?

How do I find the area to the right of a z-score?

How do I find the area between two z-scores?

Why do I need both a negative and a positive z-table?

What if my z-score has more than two decimal places or is beyond ±3.49?

Related tools

Z-score calculator

Empirical rule calculator

Normal distribution calculator

T-table (critical values)