Calculate a standard score, percentile position, deviation from the mean, or reverse-calculate a raw value using a known Z-score.
Enter your statistical values below.
Complete the required fields and select Calculate to view the Z-score, percentile, deviation, and interpretation.
Understand where a value sits within a normal distribution instead of receiving only a single unexplained number.
Calculate the number of standard deviations separating a raw value from the dataset mean.
View the approximate percentage of values expected to fall below and above your result.
Enter a known Z-score, mean, and standard deviation to calculate the corresponding raw value.
The calculator standardizes your raw value so it can be compared with other observations in the distribution.
Add the individual observation or test score that you want to compare with the overall dataset.
Enter the dataset mean and standard deviation. The standard deviation must be greater than zero.
View the Z-score, approximate percentile, deviation from the mean, and a plain-language interpretation.
A Z-score, also called a standard score, indicates how far a specific value is from the mean of a dataset. The distance is measured in standard deviations rather than in the original units of the data.
This standardization makes it easier to compare values from different datasets. For example, a student can use a Z-score to compare performance across two exams with different averages and scoring ranges.
Suppose a test score is 85, the class mean is 70, and the standard deviation is 10. Subtracting the mean from the score gives 15. Dividing 15 by 10 produces a Z-score of 1.5.
This means the test score is 1.5 standard deviations above the class average. In an approximately normal distribution, it is near the 93rd percentile.
Z-scores are commonly used in statistics, education, psychology, finance, scientific research, quality control, medical studies, and data analysis. They can help identify unusual observations, compare results, estimate probabilities, and detect possible outliers.
Find clear answers to common questions about standard scores, percentiles, and normal distributions.
A Z-score measures how many standard deviations a particular value is above or below the mean. It is also known as a standard score.
A positive Z-score means that the raw value is higher than the mean. The larger the positive Z-score, the farther the value is above the mean.
A negative Z-score means that the raw value is below the mean. For example, a Z-score of -1.5 is 1.5 standard deviations below the mean.
A Z-score below -2 or above 2 is often considered relatively unusual. Scores below -3 or above 3 may be treated as potential outliers, depending on the subject and dataset.
Yes. Select the Calculate Raw Score mode, then enter the known Z-score, mean, and standard deviation. The calculator uses x = μ + zσ.
The Z-score formula divides by the standard deviation. Division by zero is undefined, so a standard score cannot be calculated when the standard deviation is zero.
The displayed percentile is an approximation based on the standard normal distribution. It is most meaningful when the original data is normally or approximately normally distributed.