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Percentile Calculator (Z-score)

A percentile shows how a value compares to the rest of a dataset โ€” for example a test score, height, or any other trait that is approximately normally distributed. Enter your value along with the mean and standard deviation of the reference group to find your percentile.

Result

76.2

Percentile

Z-score
0.714
How this was calculated
  1. 1Calculate the z-score: (value โˆ’ mean) รท standard deviation(180 โˆ’ 175) รท 7 = 0.714
  2. 2Convert the z-score to a percentile

Formula

Z = (value โˆ’ mean) รท standard deviation, then percentile via the normal distribution

The z-score expresses how many standard deviations a value lies from the mean. A z-score of 0 is exactly average (50th percentile), +1 is well above average (roughly the 84th percentile), and โˆ’1 well below (roughly the 16th percentile). This calculator converts the z-score to a percentile using the cumulative normal distribution.

Worked examples

Value 180, mean 175, standard deviation 7

โ†’ Z โ‰ˆ 0.71 โ†’ roughly the 76th percentile.

Common mistakes

  • Using a mean and standard deviation that donโ€™t match the right reference group (for example applying a national average to a very specific subgroup).

Important to know

  • This calculator has no built-in population statistics. Look up a reliable mean and standard deviation from an official source, such as your national statistics office.

Limitations

  • This calculation assumes a normal distribution. Not every trait is normally distributed, which affects how accurate the percentile is.

When to use it

  • Comparing a test score against the rest of the class or country.

Frequently asked questions

Where do I find the mean and standard deviation of a group?

National statistics offices publish this for things like height, income and weight.

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