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Z-Score Calculator

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Enter a value, the mean, and standard deviation of a dataset to find its z-score and corresponding percentile.

Z-Score Calculator

Live
Z-score
1.00
Percentile
84.13%
Interpretation
1.00 SD above the mean
Assumes a normal (bell curve) distribution - the standard assumption behind z-scores and percentiles.

The formula

Z-score = (Value - Mean) / Standard deviation Percentile = Normal distribution CDF of the z-score
Example

A test score of 85, with a class mean of 75 and standard deviation of 10: z = (85-75)/10 = 1.00, placing that score at roughly the 84th percentile.

Step-by-step guide

  1. Enter the specific value you're evaluating.
  2. Enter the dataset's mean and standard deviation - use our Standard Deviation Calculator first if you need to compute these from raw data.
  3. Read the z-score and percentile.

What a z-score actually tells you

A z-score measures how many standard deviations a value sits above or below the mean - a simple way to compare a single result against an entire distribution, regardless of the original units. A z-score of 0 means exactly average; positive values are above average, negative values are below. Because it's standardized, a z-score also makes it possible to fairly compare values from completely different scales - like comparing a test score against a height measurement - since both get converted to the same "distance from average" language.

Common mistakes

Using the sample standard deviation formula when a population standard deviation was intended, or vice versa - the two use slightly different formulas, and mixing them up introduces a small but real error.
Assuming the percentile conversion applies to any distribution shape - it specifically assumes a normal (bell curve) distribution, which doesn't perfectly describe every real-world dataset.

Frequently asked questions

What does a negative z-score mean?

It means the value falls below the mean - a z-score of -1 is one standard deviation below average, corresponding to roughly the 16th percentile in a normal distribution.

What's considered an unusually high or low z-score?

A z-score beyond ±2 is often considered notably unusual in a normal distribution, since about 95% of values typically fall within 2 standard deviations of the mean - beyond ±3 is quite rare, capturing over 99.7% of a normal distribution within that range.

How is a z-score different from a percentile?

A z-score describes distance from the mean in standard deviation units, while a percentile describes the percentage of values falling below a given point - this calculator converts between the two directly, since one can be derived from the other under a normal distribution.

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