How to find the Z score from the p value.

An online Z score calculator helps you find a Z-score from a given raw value. This Z value calculator can also help you calculate Z scores using:

A raw data point
Sample mean and size
A data sample
A given ‘P’ value

Read this informative content to learn how to calculate the Z score, its standard formula, Z score statistics table, and more. You can also try our online critical value calculator to calculate critical values for different distributions. Read on!

What is Z Score (Statistics)?

The Z score, also called the standard score, normal score, or Z value, describes how far a raw data point is from the mean in terms of standard deviations. In statistics, the Z score indicates how much a value deviates from the mean. It can be positive or negative:

A value above the mean has a positive Z score.
A value below the mean has a negative Z score.
A Z score of zero equals the mean.

For example, a Z score of +2 means the data point is two standard deviations above the mean.

Z Score Formula:

The Z score is calculated by subtracting the population mean from the raw data and dividing by the standard deviation:

z = (x - µ) / σ

Where:

x = raw data value
µ = population mean
σ = standard deviation of the data

When the population mean is known:

z = (Ẋ - µ) / (σ / √n)

Where:

Ẋ = mean of the sample or population data points
n = sample size

Z-Score Table:

The Z score table shows the proportion of the population that lies above or below a given Z value. Simply calculate your Z statistic using a Z score calculator and find its corresponding value in the table.

Z Score Table (Right):

The Z-table for the normal distribution shows the area to the right of the curve. You can use it to determine the probability or area between Z = 0 and any positive (+) Z value.

z	0.00	0.01	0.02	0.03	0.04	0.05	0.06	0.07	0.08	0.09
0.0	0.0000	0.0040	0.0080	0.0120	0.0160	0.0199	0.0239	0.0279	0.0319	0.0359
0.1	0.0398	0.0438	0.0478	0.0517	0.0557	0.0596	0.0636	0.0675	0.0714	0.0753
0.2	0.0793	0.0832	0.0871	0.0910	0.0948	0.0987	0.1026	0.1064	0.1103	0.1141
0.3	0.1179	0.1217	0.1255	0.1293	0.1331	0.1368	0.1406	0.1443	0.1480	0.1517
0.4	0.1554	0.1591	0.1628	0.1664	0.1700	0.1736	0.1772	0.1808	0.1844	0.1879
0.5	0.1915	0.1950	0.1985	0.2019	0.2054	0.2088	0.2123	0.2157	0.2190	0.2224
0.6	0.2257	0.2291	0.2324	0.2357	0.2389	0.2422	0.2454	0.2486	0.2517	0.2549
0.7	0.2580	0.2611	0.2642	0.2673	0.2704	0.2734	0.2764	0.2794	0.2823	0.2852
0.8	0.2881	0.2910	0.2939	0.2967	0.2995	0.3023	0.3051	0.3078	0.3106	0.3133
0.9	0.3159	0.3186	0.3212	0.3238	0.3264	0.3289	0.3315	0.3340	0.3365	0.3389
1.0	0.3413	0.3438	0.3461	0.3485	0.3508	0.3531	0.3554	0.3577	0.3599	0.3621
1.1	0.3643	0.3665	0.3686	0.3708	0.3729	0.3749	0.3770	0.3790	0.3810	0.3830
1.2	0.3849	0.3869	0.3888	0.3907	0.3925	0.3944	0.3962	0.3980	0.3997	0.4015
1.3	0.4032	0.4049	0.4066	0.4082	0.4099	0.4115	0.4131	0.4147	0.4162	0.4177
1.4	0.4192	0.4207	0.4222	0.4236	0.4251	0.4265	0.4279	0.4292	0.4306	0.4319
1.5	0.4332	0.4345	0.4357	0.4370	0.4382	0.4394	0.4406	0.4418	0.4429	0.4441
1.6	0.4452	0.4463	0.4474	0.4484	0.4495	0.4505	0.4515	0.4525	0.4535	0.4545
1.7	0.4554	0.4564	0.4573	0.4582	0.4591	0.4599	0.4608	0.4616	0.4625	0.4633
1.8	0.4641	0.4649	0.4656	0.4664	0.4671	0.4678	0.4686	0.4693	0.4699	0.4706
1.9	0.4713	0.4719	0.4726	0.4732	0.4738	0.4744	0.4750	0.4756	0.4761	0.4767
2.0	0.4772	0.4778	0.4783	0.4788	0.4793	0.4798	0.4803	0.4808	0.4812	0.4817
2.1	0.4821	0.4826	0.4830	0.4834	0.4838	0.4842	0.4846	0.4850	0.4854	0.4857
2.2	0.4861	0.4864	0.4868	0.4871	0.4875	0.4878	0.4881	0.4884	0.4887	0.4890
2.3	0.4893	0.4896	0.4898	0.4901	0.4904	0.4906	0.4909	0.4911	0.4913	0.4916
2.4	0.4918	0.4920	0.4922	0.4925	0.4927	0.4929	0.4931	0.4932	0.4934	0.4936
2.5	0.4938	0.4940	0.4941	0.4943	0.4945	0.4946	0.4948	0.4949	0.4951	0.4952
2.6	0.4953	0.4955	0.4956	0.4957	0.4959	0.4960	0.4961	0.4962	0.4963	0.4964
2.7	0.4965	0.4966	0.4967	0.4968	0.4969	0.4970	0.4971	0.4972	0.4973	0.4974
2.8	0.4974	0.4975	0.4976	0.4977	0.4977	0.4978	0.4979	0.4979	0.4980	0.4981
2.9	0.4981	0.4982	0.4982	0.4983	0.4984	0.4984	0.4985	0.4985	0.4986	0.4986
3.0	0.4987	0.4987	0.4987	0.4988	0.4988	0.4989	0.4989	0.4989	0.4990	0.4990
3.1	0.4990	0.4991	0.4991	0.4991	0.4992	0.4992	0.4992	0.4992	0.4993	0.4993
3.2	0.4993	0.4993	0.4994	0.4994	0.4994	0.4994	0.4994	0.4995	0.4995	0.4995
3.3	0.4995	0.4995	0.4995	0.4996	0.4996	0.4996	0.4996	0.4996	0.4996	0.4997
3.4	0.4997	0.4997	0.4997	0.4997	0.4997	0.4997	0.4997	0.4997	0.4997	0.4998
3.5	0.4998	0.4998	0.4998	0.4998	0.4998	0.4998	0.4998	0.4998	0.4998	0.4998
3.6	0.4998	0.4998	0.4999	0.4999	0.4999	0.4999	0.4999	0.4999	0.4999	0.4999
3.7	0.4999	0.4999	0.4999	0.4999	0.4999	0.4999	0.4999	0.4999	0.4999	0.4999
3.8	0.4999	0.4999	0.4999	0.4999	0.4999	0.4999	0.4999	0.4999	0.4999	0.4999

Z Score Table (Left):

The left z-table shows the area to the left of Z.

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	0.0120	0.0160	0.0199	0.5239	0.0279	0.0319	0.0359
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	0.6064	0.1064	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

Obtain the Z statistic by using the calculator and locate it in the corresponding Z table.

Z Scores and Standard Deviations:

The Z score represents the number of standard deviations a value is from the mean.

For example:

A Z score of -3.1 indicates the value is 3.1 standard deviations below the mean, while a Z score of 4 indicates it is 4 standard deviations above the mean. The standardized value (Z score) shows the position of a data point on the normal distribution curve.

How is Z Score Used in Real Life?

The Z score represents a number’s "relative standing" within a dataset. Relative standing measures how many standard deviations a value is above or below the mean. For instance, consider a dataset of heights of 10-year-old girls; a Z score tells you how tall a particular girl is relative to the group.

How to Find Z Score (Step-by-Step):

Calculating the Z score manually is straightforward if you know the formula. Here’s a solved example for better understanding. You can also use our Z score calculator to compute the Z statistic for any data point accurately, with detailed outcomes and graphs.

Example:

Suppose a dataset has a mean (µ) of 4 and a standard deviation (σ) of 2. What is the Z score for a value of 9?

Solution:

Use the Z score formula:

z = (x - µ) / σ

Given:

x = 9, µ = 4, σ = 2

Calculation:

z = (9 - 4) / 2

z = 5 / 2

z = 2.5

Thus, the Z score of the value 9 is 2.5. You can also calculate Z scores for different data points with our calculator to get accurate results along with visual graphs.

How to Use Z Score Calculator:

Calculating the Z score manually can be time-consuming. Thankfully, the free online Z score calculator computes the Z value for any raw score in just a few seconds. Here's how to use it:

Inputs:

Choose the statistical parameter for which you want to calculate the Z score.
Enter all the data according to the selected parameter.
Click the calculate button to get the results.

Outputs: The Z score calculator provides:

Z score of the input dataset
Z score graph
Left-tailed p-value
Right-tailed p-value
Two-tailed p-value
Two-tailed confidence level
Step-by-step calculation

Note: No matter which point you use to calculate the Z score, the calculator automatically computes the standard statistical parameters based on the entered data.

Conclusion:

Now you know how our Z score calculator helps you determine the standardized Z value quickly and accurately. In investing and finance, standard deviation (SD) and Z scores are useful for analyzing market volatility. A higher SD indicates that price movements vary widely over a given period. The Z score shows how typical or atypical a particular value is compared to historical data. This Z score calculator is designed to help statisticians, students, and anyone else solve their Z statistics problems efficiently.

References:

From the authorized source of Wikipedia: Definition & applications. From the site of Investopedia: Standard deviation & Z score. From the site of Khan Academy: General formulas for the calculation of Z score.