Z Score Calculator

A Z-score is a statistical measure that shows how a single value compares to other values in a group. Researchers, Scientists, and Statisticians used it to standardize and compare data points from different groups. 

However, calculating the Z-score manually can be time-consuming and prone to errors. That’s where our z score calculator comes in handy. Whether you are in finance, a student, or anyone else, you can easily use our calculator as it speeds up the calculation process and provides quick accurate results. 

What do you mean by Z Score? 

The Z-score, also termed as the standard score or z value, is a number that shows how many standard deviations a data point is from the mean or expected value of a distribution. 

It’s called standard because it is calculated using the standard normal distribution, where the mean is zero and the standard deviation is 1. This helps show how much a data point differs from the average in a clear way. 

Z-scores are important in statistics, particularly in z-tests to determine confidence intervals. Because z-scores standardize measurements, they allow for comparing data across various scales, serving major roles in practical applications and scientific research.

What is a Z Score Calculator? 

A z score calculator is an online free tool that uses a standard formula to calculate a z statistic based on a raw score, along with a known or estimated mean and standard deviation of a distribution. 

If you have the variance in place of the standard deviation, you can calculate it by taking its square root. The calculator also offers probabilities for various sections under the standard normal curve, which are used for one-tailed or two-tailed tests. These probabilities are calculated based on the standard normal cumulative distribution function (CDF).

Benefits of Using This Calculator 

The z score calculator provides multiple advantages that make it easier to analyze and understand statistical data. The following are some benefits that our calculator offers: 

• Quick Comparison: The calculator quickly compares how a specific score relates to the mean in a dataset. By calculating the z-value, you can easily understand the relative position of that score within the dataset.
• Transparency: By providing a clear breakdown of the z-value calculation, the calculator promotes transparency in statistical analysis. Users can easily understand how data points relate to the mean and what influences the scores’ calculation. 
• Accuracy: The z score table calculator makes the calculation process easy, reducing the likelihood of manual errors and saving time in data analysis. This allows researchers, analysts, and professionals to focus on interpreting results and gaining insights. 
• Consistency: The calculator saves time by automating calculations. With a few inputs, you can easily determine standardized scores, allowing you more time to focus on other tasks. 

The Z Score Table 

A z table, also called a standard normal table or unit normal table, contains standardized values used to find out the probability that a statistic falls below, above, or between points in the normal distribution. A z score of 0 means the point is exactly in the mean. 

On a standard normal distribution graph, z=0 marks the center of the curve. If a z-value is positive, it tells that the point is to the right of the mean and if it’s negative, the point is to the left. 

The table below displays the area between z=0 and a specific z score. 

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

How to Calculate the Z Score? 

When you calculate a z-score you convert a raw data point into a standardized score that fits a standard normal distribution. The following are the steps you can use to calculate the z score: 

• Subtract the mean (μ) from the raw score. 
• Divide the result by the standard deviation (σ) to get the z score. 

A z score calculator uses the formula: 

z = (x – μ) / σ

For example, let’s suppose you scored 85 on a test. In your class, the average score (mean) is 75, and the standard deviation is 10. To find the z-score, you use the formula z = (x – μ) / σ. 

Here, x represents your score, which is 85. The mean, μ, is 75, and the standard deviation, σ, is 10. Begin by subtracting the mean from your score: 85 – 75 = 10. This tells you how much higher your score is compared to the average score. 

Next, divide this difference by the standard deviation: 10 / 10 = 1. So, the z-score is 1. This means your score is 1 standard deviation above the mean, showing you performed better than the average student by a margin of one standard deviation.

How to use a Z Score Calculator? 

A z score probability calculator determined the standard score of any raw data. The z-value tells how many standard deviations a raw score is above or below the mean of the data. Follow the steps given below to use our calculator: 

1. Input the values of the raw score, the mean, and the standard deviation into the respective boxes in the calculator. 
2. Press the “Calculate” button to begin the calculation process. 
3. The calculated score will be displayed on your screen.

The z score to critical calculator makes the calculation process fast, showing the z-score in just a fraction of a second. 

Example of Using a Z Score Calculator

Let’s say you need to calculate the z-value for a raw score of 20, with a mean of 15, and a standard deviation of 5. To figure out the z-score first subtract the mean (15) from the raw score (20), which results in 5. 

Next, divide this difference by the standard deviation (5). The calculation is (20 – 15) / 5, which equals 1. Therefore, the Z-score is 1. A positive Z-score shows that the raw score of 20 is above the mean.

You can verify this by using a z score to percentile calculator. Enter the raw score (20), mean (15), and standard deviation (5) into the calculator, and it will confirm that the Z-score is 1, showing the raw score is above the mean.

Frequently Asked Questions 

How do you interpret the z-score? 

The z-score tells how far a data point is from the average, measured in standard deviations. A positive z-score means the data point is above the average, while a negative z-score means it’s below. For example, a z-score of 1 indicates the data point is totally 1 standard deviation above the average.

How accurate is a z score calculator? 

Our calculator offers accurate z-scores because it follows a standard formula to find the z-value. It measures how much a data point differs from the average using standard deviations. 

How can I find the p-value from the z-score? 

The simplest method to find the p-value from a z-score is by using a z-score table. The calculation itself involves determining the cumulative area under the curve of a normal distribution.

Are z scores limited to -1 or greater than 1?

Yes, z-scores can be bigger than 1 or less than -1, showing how far a value deviates from the mean using standard deviations.