Z-Score Calculator
Standardise a value. Enter the raw value, the mean and the standard deviation to get its z-score.
Learn how to calculate it yourselfEnter your values
Results update as you type.
How to enter your data
Enter one number in each box: the value you want to standardize, the reference mean, and the reference standard deviation. The standard deviation must be greater than zero. Use plain numbers without units; this calculator does not accept a raw data list.
Z-score
- Percentile
- 93.3%
The Z-Score Calculator tells you how far one number sits above or below the average of a group, measured in "standard deviations" (a standard way of describing how spread out the numbers are). A z-score of 0 means the number is exactly average, a positive score means it is above average, and a negative score means it is below. The bigger the score, the more unusual that number is compared with the rest of the group.
Calculate it yourself
Example: a value of 85 comes from a distribution with mean 70 and standard deviation 10.
Follow this worked example, then repeat the steps with your own numbers.
Find the distance from the mean
x − mean = 85 − 70 = 15Divide by the standard deviation
z = (x − mean) ÷ SD = 15 ÷ 10 = 1.5Check the result in the original units
Mean + z × SD = 70 + 1.5 × 10 = 85The value is 1.5 standard deviations above the mean. A negative z-score would be below the mean.
Look up the normal percentile
Φ(1.5) × 100 ≈ 0.93319 × 100 ≈ 93.3%A standard normal table gives the area below 1.5. This percentile assumes a normal distribution; it is not a rank calculated from raw data.
Use your PaperSurvey.io results
Use a question’s mean and standard deviation to standardize an individual response in this calculator.
Where it is used
- Teachers: A teacher enters every pupil's test score and checks how far one pupil's mark sits above or below the class average.
- Small-business owners: A cafe owner enters daily sales for the month to see whether one unusually quiet day was really out of the ordinary.
- HR and staff-survey teams: An HR officer enters each department's staff satisfaction rating to spot a team whose result is far from the company average.
What is a z-score?
A z-score expresses how many standard deviations a value sits above or below the mean. A z-score of 0 is exactly average; +1 is one standard deviation above the mean. It lets you compare values from different scales.
When should you use it?
Use it when you have a group of numbers and want to know whether one of them is normal or unusual compared with the rest. It works well for test scores, survey ratings, prices, times, or any measurement where you already have several results to compare. Instead of guessing whether a number is high or low, the z-score gives you a clear figure. It is most useful when you have a good handful of numbers, roughly ten or more, so that the average and the spread are meaningful.
What does the result mean?
The result is the z-score. Zero means the number matches the group average exactly. A score of plus 1 means it sits one standard deviation above average, and minus 1 means one below. As a rough guide, about two thirds of everyday values fall between minus 1 and plus 1, and about 95 percent fall between minus 2 and plus 2. So a score beyond plus or minus 2 is fairly unusual, and beyond plus or minus 3 is rare and worth a closer look.
Mistakes to avoid
Use a value, mean, and standard deviation measured on the same scale. Enter a positive standard deviation, and check for typos. The displayed percentile uses a normal-distribution model; it may not match an empirical percentile for skewed or otherwise non-normal data. A positive or negative z-score is not inherently good or bad.
How to use this calculator
- Enter the value you want to standardize in Value (x).
- Enter the reference mean in Mean.
- Enter a positive reference standard deviation in Standard deviation, using the same measurement scale.
- Read the z-score and the normal-model percentile. Interpret the percentile only when that distributional assumption is appropriate.
Worked example
Enter 85 as the value, 70 as the mean, and 10 as the standard deviation. The z-score is (85 - 70) / 10 = 1.5. The displayed percentile is about 93.3%, assuming a normal distribution; it is not an empirical rank calculated from raw data.
Frequently asked questions
What numbers do I type in?
Enter the value to standardize, the reference mean, and the reference standard deviation in their separate boxes. If you only have raw data, calculate its mean and standard deviation first.
Where do I get these numbers?
They usually come from your own records, such as a spreadsheet of scores, sales, or survey answers. If your survey was scanned in PaperSurvey, you can export the results and paste the column of numbers here.
What does a z-score of 0 mean?
It means that number is exactly equal to the average of the group. It is neither high nor low compared with the rest.
Is a high z-score good or bad?
Neither on its own. A high positive score just means the number is far above average, and a negative score means far below. Whether that is good or bad depends on what you are measuring.
What counts as an unusual score?
As a rough rule, a z-score between minus 2 and plus 2 is fairly normal. A score beyond plus or minus 2 is uncommon, and beyond plus or minus 3 is rare.
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