Find the z-score (standard score) and percentile of a value.
Calculated instantly in your browser.
How do you calculate a z-score?
A z-score is calculated with z = (x − μ) ÷ σ, where x is your value, μ the mean and σ the standard deviation. It tells you how many standard deviations a value lies from the mean. A positive z-score is above the mean, a negative one below. Example: a score of 130 with mean 100 and standard deviation 15 gives z = 2.0, around the 97.7th percentile.
Understanding your result
A positive z-score is above the mean, a negative one below. The percentile assumes the data follows a normal (bell-curve) distribution.
Formula and method
z = (x − μ) ÷ σ. The percentile is the area under the standard normal curve to the left of z.
Assumptions and limitations
This tool standardises a value using the mean and standard deviation you supply and reads a percentile from the standard normal curve. That percentile is only accurate when the data is approximately normally distributed; skewed or heavy-tailed data will be misrepresented. The standard deviation must be greater than zero, since a value of zero makes the z-score undefined.
Worked example
A score of 130 with a mean of 100 and standard deviation of 15 gives z = 2.0, around the 97.7th percentile.
How to use this tool
- Enter the value, the mean and the standard deviation.
- Read the z-score and its percentile.
Common mistakes to avoid
- Using a standard deviation of zero.
- Reading percentiles as exact for data that is not normally distributed.
About the Z-Score Calculator
The Z-Score Calculator tells you how many standard deviations a value lies from the mean, and converts that into a percentile on the normal distribution.
Who should use this tool
Statistics students, researchers and anyone comparing a result against a distribution.
Benefits
- Standardise any value against its distribution.
- Get the percentile and the probability above.
- Useful for grades, test scores and quality control.
- Private and instant.
Practical use cases
- Seeing how an exam score compares to the class.
- Spotting outliers in data.
- Converting a measurement to a percentile.
Frequently asked questions
What does a z-score of 0 mean?
It means the value is exactly equal to the mean, which sits at the 50th percentile.
Is the percentile always accurate?
The percentile assumes a normal distribution. For skewed data it is only an approximation.
Is the percentile reliable for any dataset?
No. The percentile is derived from the standard normal distribution and only holds when your data follows a roughly bell-shaped curve. For skewed distributions, small samples or data with heavy tails, the same z-score can correspond to a very different real percentile, so treat the figure as an approximation in those cases.