📐 Percentile Calculator (Z-score)

A percentile shows how a value compares to the rest of a dataset — for example a test score, height, or any other trait that is approximately normally distributed. Enter your own value along with the mean and standard deviation of the reference group, and this calculator instantly works out your z-score and matching percentile.

Percentile 76.2
Z-score 0.714
Calculate the z-score: (value − mean) ÷ standard deviation: (180 − 175) ÷ 7 = 0.714
Convert the z-score to a percentile: = 76.2e percentiel

Formula

Z = (value − mean) ÷ 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 −1 well below (roughly the 16th percentile). This calculator converts the z-score to a percentile using the cumulative normal distribution (the Abramowitz-Stegun approximation).

Steps

  1. 1Enter your own value, such as a test score or height.
  2. 2Enter the mean and standard deviation of the reference group.
  3. 3Read off the z-score and the matching percentile.

Z-score to percentile

Z-scorePercentileMeaning
−22.3rdWell below average
−115.9thBelow average
050thExactly average
+184.1stAbove average
+297.7thWell above average

Rules of thumb for a normal distribution; use the calculator above for your own value.

warnings

  • 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.

commonMistakes

  • Using a mean and standard deviation that don't match the right reference group (for example applying a national average to a very specific subgroup).
  • Thinking a percentile is the same as a percentage of the maximum, when it actually indicates what percentage of the group you outperform.
  • Treating the result as absolute truth when the assumption of a normal distribution doesn't always hold.

useCases

  • Comparing a test score against the rest of the class or country.
  • Interpreting growth charts or medical measurements relative to a reference group.
  • Putting job application or assessment results in perspective relative to other candidates.