Enter a value along with the mean and standard deviation of its distribution to calculate its z-score and corresponding percentile.
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A z-score measures how many standard deviations a value is from the mean: z = (value − mean) ÷ standard deviation. This calculator then converts that z-score into a percentile using the standard normal cumulative distribution function, showing what percentage of values in a normal distribution fall below your entered value.
For a test score of 85, with a class mean of 75 and standard deviation of 10: z = (85 − 75) ÷ 10 = 1, meaning the score is exactly 1 standard deviation above the mean. Converting that z-score to a percentile using the standard normal distribution gives approximately the 84.13th percentile, so this score is higher than about 84% of the distribution, assuming scores are normally distributed.
Applying the percentile conversion to data that isn't actually normally distributed, the z-score itself is valid for any distribution, but the percentile figure specifically assumes a bell-curve shape, and can be misleading for skewed data.
Confusing z-score with percentile, a z-score of 1 doesn't mean the 1st percentile, it means 1 standard deviation above the mean, which actually corresponds to roughly the 84th percentile.
Using population standard deviation when the data is really a sample, or vice versa, the standard deviation entered should match how it was actually calculated, since sample and population versions can differ, especially for small data sets.
A negative z-score means the value is below the mean, a positive z-score means it's above the mean.
Yes, the percentile conversion assumes the underlying data follows a normal (bell-curve) distribution. The z-score itself is valid for any distribution, but the percentile figure is only accurate when that assumption holds.
Confidence Interval Calculator
Calculate a confidence interval and margin of error from a sample mean and standard deviation.
Standard Deviation Calculator
Calculate mean, variance and standard deviation from a data set.
Sample Size Calculator
Calculate the survey sample size needed for a target confidence level and margin of error.
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