Z-Score Calculator
Calculate a z-score from a value, mean, and standard deviation, plus the percentile and two-tailed p-value from the standard normal distribution.
Calculator by Toolsloft ↗- Z-score
- 1
- Percentile
- 84.134474%
- Two-tailed p-value
- 0.317311
Turn a raw value into a z-score, showing how many standard deviations it sits above or below the mean. Enter the value, the mean, and the standard deviation to get the z-score, the percentile it falls at on a normal curve, and the two-tailed p-value. Useful for test scores, quality control, and reading standardized results.
How this is calculated
The z-score is (value minus mean) divided by the standard deviation, the standard definition of a standardized score. The percentile and p-value come from the standard normal cumulative distribution function, computed with the error function, so the percentile is the area under the normal curve below the value.
How to use
- Enter the value you want to standardize.
- Enter the mean and standard deviation of the data.
- Read the z-score, the percentile, and the two-tailed p-value.
Examples
- One SD above:
value 115, mean 100, SD 15 gives z = 1 - One SD below:
value 85, mean 100, SD 15 gives z = -1 - At the mean:
value 100, mean 100 gives z = 0 (50th percentile)
FAQ
- What does a z-score tell you?
- It tells you how far a value is from the mean, measured in standard deviations. A z-score of 2 means the value is two standard deviations above the mean, and a negative z-score means it is below the mean.
- What is the percentile shown here?
- It is the share of a normal distribution that falls below your value. A z-score of 1 sits at about the 84th percentile, meaning roughly 84 percent of values are lower.