Z Score Table

Standard normal table: P(Z ≤ z) for z ≥ 0

Read the row for the first decimal of z, for example 1.9, then the column for the second decimal, for example 0.06. The cell gives the share of the distribution below z. For z = 1.96, the row is 1.9 and the column is 0.06. For a negative z, subtract the table value from 1: P(Z ≤ −1.96) = 1 − 0.9750 = 0.0250.

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

Two-sided confidence	Area in each tail	Critical z
80%	0.1000	1.2816
90%	0.0500	1.6449
95%	0.0250	1.9600
98%	0.0100	2.3263
99%	0.0050	2.5758
99.9%	0.0005	3.2905

Two-sided confidence

Area in each tail

Critical z

80%

0.1000

1.2816

90%

0.0500

1.6449

95%

0.0250

1.9600

98%

0.0100

2.3263

99%

0.0050

2.5758

99.9%

0.0005

3.2905

📊 Z Score Table — Free Online Tool

Standard normal table of z scores and cumulative probabilities. A z score table lists P(Z ≤ z), the probability that a standard normal variable falls below z, for z from 0 to 3.49 in steps of 0.01. Negative z values follow from symmetry, so the positive table covers the whole distribution. This page prints the table to four decimals, lists the critical z values used in confidence intervals and tests, and runs the lookup in reverse: enter a percentile and get the z score at that point. Every cell is computed from the normal distribution rather than copied from a printed book.

How to use it

Find the row for the first decimal of z, such as 1.9.
Find the column for the second decimal, such as 0.06.
Read the cell. 0.9750 means 97.5% of values fall below z = 1.96.
For the reverse lookup, enter a percentile in the lookup box to get its z score.

🚀 Why use this Z Score Table tool?

A z table puts any normal distribution on one common scale. Once a value is standardized to a z score, one table gives its percentile, so the standard cases need no software. 100% free, no registration, and complete privacy — everything runs locally in your browser, so your data never touches a server.

Key Features

📊Table for z from 0 to 3.49

35 rows of z in tenths and 10 columns of hundredths. Every cell is P(Z ≤ z) to four decimals.

↔️Both directions

Look up a probability for a z score, or the z score for a percentile, with a check value.

🎯Critical values

Two-sided critical z for 80%, 90%, 95%, 98%, 99% and 99.9% confidence, with the area left in each tail.

🔒Computed, not copied

The table is calculated in your browser from the standard normal CDF and checked against published values in the test suite.

Popular Use Cases

Statistics class

• Read P(Z ≤ z) without software
• Check a textbook answer
• Find a critical value for a test

Research and QA

• Convert a measurement to a percentile
• Flag values beyond ±3 standard deviations
• Compare results on different scales

Confidence intervals

• Find z for a 95% interval
• Compare z with t critical values
• Size a sample when sigma is known

What It Handles

Table

✓ z from 0.00 to 3.49
✓ P(Z ≤ z) to four decimals
✓ Hundredths columns

Lookup

✓ z to left and right tail
✓ Percentile to z
✓ Check value for each result

Method

✓ Standard normal CDF
✓ Runs in the browser
✓ Nothing sent to a server

Related Tools

Z Score Calculator →

Z score, percentile and p-values for a value, mean and standard deviation.

P-Value Calculator →

P-values from a z or t test statistic, one-tailed and two-tailed.

Confidence Interval Calculator →

Confidence intervals for a mean and a proportion, using z or t.

Standard Deviation Calculator →

Sample and population standard deviation and variance for a list.

Sources & References

NIST/SEMATECH e-Handbook of Statistical Methods

Frequently Asked Questions

What does a z table show?

It shows the cumulative probability P(Z ≤ z) for a standard normal variable, which is the share of a normal distribution below z. The cell at row 1.9 and column 0.06 is 0.9750, so 97.5% of values lie below z = 1.96.

How do I use a z table for a z score between two rows?

Round z to two decimals and read the nearest cell, or use the lookup above for a value to four decimals. For most work the rounding error is far smaller than the uncertainty in the data.

What is the difference between a z table and a t table?

A z table assumes the population standard deviation is known or the sample is large. A t table uses n − 1 degrees of freedom and has heavier tails, so its critical values are larger for small samples. From about 30 degrees of freedom the two are close.

Why does the table stop at 3.49?

Beyond 3.49 each tail holds less than 0.0003 of the distribution (P(Z > 3.49) is about 0.00024), so the table covers the range that matters for most tests. The lookup above accepts any z score, including negative values and values beyond 3.49.

How accurate is the table?

Each cell is computed from the normal distribution with a regularized incomplete gamma function and checked in our test suite against published reference values to within 1e-9. It is rounded to four decimals for display.

🎓 Pro Tips

Tip 1: For a two-sided 95% interval, use z = 1.96. The area in each tail is 0.025, so the cumulative value is 0.975.
Tip 2: The right tail is 1 minus the table value: P(Z ≥ 1.96) = 1 − 0.9750 = 0.0250.
Tip 3: For a negative z, use symmetry, Φ(−z) = 1 − Φ(z), since the table lists z from 0 upward.

Left tail, P(Z ≤ z)	0.975002
Right tail, P(Z ≥ z)	0.024998
Table value to 4 decimals	0.9750

Standard normal probabilities, critical values and percentile to z

Look up a z score

Look up a z score from a percentile