About Z-Score Calculator
This z-score calculator measures how far a value sits from the mean of your list, in units of the list standard deviation. It is free, needs no sign-up and runs in your browser, so nothing you enter is uploaded.
Paste your data, then type the value you want to standardise in the z-score box. The page computes the mean and standard deviation of your list and shows the line z = (x - mean) / SD with the numbers filled in. The switch between sample and population changes the SD, and therefore the z-score, so pick the one that matches your data.
There is no field for a known mean and standard deviation: the z-score always comes from the list in the data box. If you only know a mean and SD, you can calculate z by hand with the formula below. The calculator gives the z-score only and does not convert it to a percentile or probability from a normal table.
How to use Z-Score Calculator
- Paste or type your numbers in the data box. Commas, semicolons, spaces and line breaks all work as separators, and the line under the box tells you how many values were read.
- Choose Sample (n - 1) if your numbers are a sample of a larger group, or Population (n) if they are every value you care about.
- Pick the quartile method if you need to match a textbook, Excel or R. The quartiles, the IQR, the fences, the box plot and the percentile box all follow the same choice.
- For grouped data, switch Input type to Grouped data and enter one class per line, such as 10-20 5, meaning the class 10 to 20 with a frequency of 5.
- Read the result cards. The card for the page you opened is outlined, for example the standard deviation on the standard deviation page.
- For a z-score or percentile, type a value or a percentage in the matching box and read the line below it.
- For a confidence interval, pick 90%, 95% or 99%. For correlation and regression, paste a second list of the same length in the Y box.
- Open Steps and formulas at the bottom to see the calculation written out with your numbers.
Features
- Count, sum, mean, median, mode (all tied values), minimum, maximum and range.
- Sample or population variance and standard deviation with one switch, plus the standard error of the mean.
- Quartiles by a method you choose (inclusive, exclusive or linear), the same method for the percentile box, the interquartile range, outlier fences and a list of flagged outliers.
- Grouped data: class intervals with frequencies give the mean, variance, SD and the median by interpolation inside the median class.
- A box plot with whiskers and outlier dots, and a frequency table with relative and cumulative columns.
- A warning that lists every item that was left out because it is not a number.
- Skewness and excess kurtosis, using the adjusted forms for a sample and the plain moment forms for a population.
- z-score of any value against your data and any percentile by linear interpolation.
- Confidence interval for the mean at 90%, 95% or 99%, using the t distribution with n - 1 degrees of freedom.
- Pearson r, R squared, slope and intercept for paired X and Y lists.
- A histogram with axis titles and a values table for screen readers, and a written-out working for the mean, variance, standard deviation, range and IQR.
- Fifteen focused pages (standard deviation, variance, quartiles, five-number summary, grouped data, z-score and more) that open the same tool with the matching result outlined.
Z-score formula
Subtract the mean from the value and divide by the standard deviation. A positive z is above the mean, a negative z is below it, and 0 is exactly at the mean.
z = (x − mean) / SDWorked examples
Scores 62, 68, 70, 74, 76, 80, 85, 91; x = 91 gives mean 75.75. Sample SD 9.4226, z = 1.6184. Population SD 8.8141, z = 1.7302.
The score of 91 is about 1.6 standard deviations above the mean.
4, 8, 15, 16, 23, 42; x = 23 gives mean 18. Sample SD 13.4907, z = 0.3706. Population SD 12.3153, z = 0.4060.
Good to know
Entering your data
Separate values with commas, semicolons, spaces or line breaks and use a dot as the decimal mark. Text that is not a number is skipped, so check the "values parsed" count under the box matches what you pasted.
Privacy: how it works
- Everything is calculated by JavaScript running in your own browser tab. Your numbers are not sent to Ulkaa or to any other server, and the page makes no network requests while you type.
- There is no account and nothing is stored. Closing or reloading the tab clears what you entered.
Tips
- If two sources give different standard deviations for the same data, check whether one divides by n and the other by n - 1 before assuming a mistake.
- Compare the mean with the median. A mean far above the median usually means a few large values are pulling it up, and the outlier fences will often show them.
- The confidence interval gets narrower with more data and wider with a higher confidence level. Try 90%, 95% and 99% on the same list to see how much.
- Correlation only measures a straight-line relationship. Two lists can have an r near 0 and still be tightly related by a curve, so look at the histogram and your data before you rely on r.
- Pair the X and Y lists by position. If they differ in length, only the first n pairs, where n is the shorter list, are used.
Frequently asked questions
Is it really free?
Yes. There is no price, no trial and no credit card. Ulkaa Tool does the work with your own device, so there is no server bill to pass on to you.
Do I need an account?
No. There is no sign-up and no login. Open the page and use it. An Ulkaa account is not needed for anything on this tool.
Does it run in my browser?
Yes. Your numbers are processed by code running in your browser tab, on your own device.
Is my data uploaded?
No. Your numbers are never sent to Ulkaa or to anyone else. You can check this yourself by watching the Network tab in your browser developer tools while you use the tool.
What does a z-score of 2 mean?
The value is 2 standard deviations above the mean. In roughly bell-shaped data about 95 percent of values fall within 2 standard deviations of the mean, so a z of 2 or more is fairly unusual.
Can I enter a mean and standard deviation directly?
No. The z-score is calculated from the list in the data box. If you already know the mean and SD, use z = (x - mean) / SD with a calculator.
Should I use the sample or population SD for a z-score?
Use population SD if your list is the entire group, and sample SD if it is a sample from a larger group. The two give slightly different z-scores, as the example shows.
More Statistics Calculator pages
- Statistics CalculatorPaste a list of numbers and get the mean, median, mode, spread, quartiles, a z-score, a confidence interval and a regression line.
- Standard Deviation CalculatorPaste your numbers and get the sample and population standard deviation with every step.
- Mean, Median and Mode CalculatorMean, median, mode and range of any list, in one view.
- Mean CalculatorThe average of a list of numbers, with the sum and count.
- Median CalculatorThe middle value of a list, with the quartiles alongside.
- Mode CalculatorThe most frequent value in a list, with ties handled.
- Variance CalculatorSample or population variance, with the sum of squares.
- Range CalculatorMinimum, maximum and range of a list of numbers.
- Confidence Interval CalculatorA t-based confidence interval for the mean of your data.
- Correlation CalculatorPearson r and R squared for two paired lists.
- Linear Regression CalculatorThe least-squares line y = mx + b for paired data.
- Quartile and IQR CalculatorQ1, median, Q3, IQR and outlier fences for a list of numbers.
- Interquartile Range (IQR) CalculatorThe IQR of your data, with Q1, Q3 and the outlier fences.