Z-Table — Standard Normal Distribution

Q: How do I read a z-table?

Find the row that matches the integer and tenths place of your z-score (e.g., 1.5 for z = 1.56). Then find the column that matches the hundredths place (e.g., 0.06). The cell value is the cumulative left-tail probability P(Z ≤ z). For z = 1.56, the value is 0.9406 — meaning 94.06% of standard normal values fall at or below 1.56.

Q: What is the difference between the positive and negative z-tables?

The positive table covers z-scores from 0.00 to 3.49, where probabilities are at or above 0.5. The negative table covers z-scores from -3.49 to -0.10, where probabilities are below 0.5. For very small negative z values between 0 and -0.10, use the positive table by symmetry: P(Z ≤ -|z|) = 1 − P(Z ≤ |z|).

Q: Does this z-table give left-tail or right-tail probability?

Left-tail. Each cell shows P(Z ≤ z), the cumulative probability that a standard normal random variable is at or below the listed z-score. To get right-tail probability, subtract from 1: P(Z ≥ z) = 1 − P(Z ≤ z).

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

Look up both z-scores, then subtract the smaller probability from the larger. For example, the area between z = -1 and z = 1 is P(Z ≤ 1) − P(Z ≤ -1) = 0.8413 − 0.1587 = 0.6826.

Q: How accurate are these values?

The values come from the standard normal cumulative distribution function computed via the Abramowitz and Stegun rational approximation, which is accurate to better than 7.5 × 10⁻⁸ — far more precise than the four-decimal display.

Q: What if my z-score has more than two decimal places?

Round to two decimals for table lookup, or use our z-score calculator for arbitrary z-score values. Linear interpolation between adjacent table cells is also a common approximation.

A standard normal z-table lists cumulative left-tail probabilities for the standard normal distribution. Each cell shows P(Z ≤ z), the probability that a standard normal random variable is at or below the corresponding z-score. Use the row for the integer and tenths place, and the column for the hundredths place. Tables cover z-scores from −3.49 to 3.49 in 0.01 increments.

Common Reference Values

z	P(Z ≤ z)	Notes
0.00	0.5000	50th percentile (mean)
1.00	0.8413	84.13 percentile rank (1 SD above mean)
1.28	0.8997	≈ 90th percentile
1.645	0.9500	95th percentile (one-tailed α = 0.05)
1.96	0.9750	97.5 percentile rank (two-tailed α = 0.05)
2.00	0.9772	97.72 percentile rank (2 SD above mean)
2.33	0.9901	≈ 99th percentile (one-tailed α = 0.01)
2.58	0.9951	≈ 99.5 percentile rank (two-tailed α = 0.01)
3.00	0.9987	99.87 percentile rank (3 SD above mean)

Positive Z-Table (z = 0.00 to 3.49)

For z-scores at or above the mean. Probabilities range from 0.5000 (at z = 0) to about 0.9998 (at z = 3.49).

P(Z ≤ z) for z ≥ 0
z	0.00	0.01	0.02	0.03	0.04	0.05	0.06	0.07	0.08	0.09
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

Negative Z-Table (z = -3.49 to -0.10)

For z-scores below the mean. Probabilities range from about 0.0002 (at z = -3.49) to about 0.4602 (at z = -0.10). For very small negative z between 0 and -0.10, use the positive table by symmetry: P(Z ≤ -|z|) = 1 − P(Z ≤ |z|).

P(Z ≤ z) for z ≤ -0.10
z	0.00	0.01	0.02	0.03	0.04	0.05	0.06	0.07	0.08	0.09
−0.1	0.4602	0.4562	0.4522	0.4483	0.4443	0.4404	0.4364	0.4325	0.4286	0.4247
−0.2	0.4207	0.4168	0.4129	0.4090	0.4052	0.4013	0.3974	0.3936	0.3897	0.3859
−0.3	0.3821	0.3783	0.3745	0.3707	0.3669	0.3632	0.3594	0.3557	0.3520	0.3483
−0.4	0.3446	0.3409	0.3372	0.3336	0.3300	0.3264	0.3228	0.3192	0.3156	0.3121
−0.5	0.3085	0.3050	0.3015	0.2981	0.2946	0.2912	0.2877	0.2843	0.2810	0.2776
−0.6	0.2743	0.2709	0.2676	0.2643	0.2611	0.2578	0.2546	0.2514	0.2483	0.2451
−0.7	0.2420	0.2389	0.2358	0.2327	0.2296	0.2266	0.2236	0.2206	0.2177	0.2148
−0.8	0.2119	0.2090	0.2061	0.2033	0.2005	0.1977	0.1949	0.1922	0.1894	0.1867
−0.9	0.1841	0.1814	0.1788	0.1762	0.1736	0.1711	0.1685	0.1660	0.1635	0.1611
−1.0	0.1587	0.1562	0.1539	0.1515	0.1492	0.1469	0.1446	0.1423	0.1401	0.1379
−1.1	0.1357	0.1335	0.1314	0.1292	0.1271	0.1251	0.1230	0.1210	0.1190	0.1170
−1.2	0.1151	0.1131	0.1112	0.1093	0.1075	0.1056	0.1038	0.1020	0.1003	0.0985
−1.3	0.0968	0.0951	0.0934	0.0918	0.0901	0.0885	0.0869	0.0853	0.0838	0.0823
−1.4	0.0808	0.0793	0.0778	0.0764	0.0749	0.0735	0.0721	0.0708	0.0694	0.0681
−1.5	0.0668	0.0655	0.0643	0.0630	0.0618	0.0606	0.0594	0.0582	0.0571	0.0559
−1.6	0.0548	0.0537	0.0526	0.0516	0.0505	0.0495	0.0485	0.0475	0.0465	0.0455
−1.7	0.0446	0.0436	0.0427	0.0418	0.0409	0.0401	0.0392	0.0384	0.0375	0.0367
−1.8	0.0359	0.0351	0.0344	0.0336	0.0329	0.0322	0.0314	0.0307	0.0301	0.0294
−1.9	0.0287	0.0281	0.0274	0.0268	0.0262	0.0256	0.0250	0.0244	0.0239	0.0233
−2.0	0.0228	0.0222	0.0217	0.0212	0.0207	0.0202	0.0197	0.0192	0.0188	0.0183
−2.1	0.0179	0.0174	0.0170	0.0166	0.0162	0.0158	0.0154	0.0150	0.0146	0.0143
−2.2	0.0139	0.0136	0.0132	0.0129	0.0125	0.0122	0.0119	0.0116	0.0113	0.0110
−2.3	0.0107	0.0104	0.0102	0.0099	0.0096	0.0094	0.0091	0.0089	0.0087	0.0084
−2.4	0.0082	0.0080	0.0078	0.0075	0.0073	0.0071	0.0069	0.0068	0.0066	0.0064
−2.5	0.0062	0.0060	0.0059	0.0057	0.0055	0.0054	0.0052	0.0051	0.0049	0.0048
−2.6	0.0047	0.0045	0.0044	0.0043	0.0041	0.0040	0.0039	0.0038	0.0037	0.0036
−2.7	0.0035	0.0034	0.0033	0.0032	0.0031	0.0030	0.0029	0.0028	0.0027	0.0026
−2.8	0.0026	0.0025	0.0024	0.0023	0.0023	0.0022	0.0021	0.0021	0.0020	0.0019
−2.9	0.0019	0.0018	0.0018	0.0017	0.0016	0.0016	0.0015	0.0015	0.0014	0.0014
−3.0	0.0013	0.0013	0.0013	0.0012	0.0012	0.0011	0.0011	0.0011	0.0010	0.0010
−3.1	0.0010	0.0009	0.0009	0.0009	0.0008	0.0008	0.0008	0.0008	0.0007	0.0007
−3.2	0.0007	0.0007	0.0006	0.0006	0.0006	0.0006	0.0006	0.0005	0.0005	0.0005
−3.3	0.0005	0.0005	0.0005	0.0004	0.0004	0.0004	0.0004	0.0004	0.0004	0.0003
−3.4	0.0003	0.0003	0.0003	0.0003	0.0003	0.0003	0.0003	0.0003	0.0003	0.0002

How to Read the Z-Table

Identify the sign of your z-score. Use the positive table if z ≥ 0 and the negative table if z < 0.
Locate the row that matches the integer and tenths place of your z-score. For z = 1.56, that row is labeled 1.5.
Locate the column that matches the hundredths place. For z = 1.56, that column is labeled 0.06.
The cell value is P(Z ≤ z). For z = 1.56, the cell reads 0.9406, meaning 94.06% of standard normal values fall at or below 1.56.
For right-tail probability, subtract from 1: P(Z ≥ 1.56) = 1 − 0.9406 = 0.0594.
For the area between two z-scores, look up both and subtract the smaller probability from the larger.

Frequently Asked Questions

How do I read a z-table?

Find the row that matches the integer and tenths place of your z-score (e.g., 1.5 for z = 1.56). Then find the column that matches the hundredths place (e.g., 0.06). The cell value is the cumulative left-tail probability P(Z ≤ z). For z = 1.56, the value is 0.9406 — meaning 94.06% of standard normal values fall at or below 1.56.

What is the difference between the positive and negative z-tables?

The positive table covers z-scores from 0.00 to 3.49, where probabilities are at or above 0.5. The negative table covers z-scores from -3.49 to -0.10, where probabilities are below 0.5. For very small negative z values between 0 and -0.10, use the positive table by symmetry: P(Z ≤ -|z|) = 1 − P(Z ≤ |z|).

Does this z-table give left-tail or right-tail probability?

Left-tail. Each cell shows P(Z ≤ z), the cumulative probability that a standard normal random variable is at or below the listed z-score. To get right-tail probability, subtract from 1: P(Z ≥ z) = 1 − P(Z ≤ z).

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

Look up both z-scores, then subtract the smaller probability from the larger. For example, the area between z = -1 and z = 1 is P(Z ≤ 1) − P(Z ≤ -1) = 0.8413 − 0.1587 = 0.6826.

How accurate are these values?

The values come from the standard normal cumulative distribution function computed via the Abramowitz and Stegun rational approximation, which is accurate to better than 7.5 × 10⁻⁸ — far more precise than the four-decimal display.

What if my z-score has more than two decimal places?

Round to two decimals for table lookup, or use our z-score calculator for arbitrary z-score values. Linear interpolation between adjacent table cells is also a common approximation.

Related Calculators

Z-Score Calculator — Probability for any tail or middle area.
Inverse Z-Score — Critical z from probability or confidence level.
Z-Score to Percentile — Convert any z-score to a percentile rank.
P-Value Calculator — One- and two-tailed p-values from a z-score.

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