Test Score Percentile Calculator

Your score

Mean score

Standard deviation

How many took the test

Result

Percentile86.07%
z-score1.083
You beat, % of the field86.1%
Ahead of you, %13.9%
Approximate rankenter the group size
What mattersThe percentile assumes scores are normally distributed. On an easy test with a ceiling the distribution is skewed and the estimate runs high.

A score means nothing on its own

Converts a test score into a percentile using the mean and standard deviation, and estimates the resulting rank.

Is seventy-eight a good score? It depends entirely on how everyone else did. If the mean is sixty-five with a spread of twelve, the result is well above average. If the mean is eighty, the same score falls below half the field.

A percentile answers that in one number: the share of participants you beat. It comes from the z-score — how many standard deviations the result sits from the mean.

What this calculator shows

The percentile and the z-score of the result
The share of participants behind you and ahead of you
An approximate rank when the group size is known

What to keep in mind

The calculation assumes scores are normally distributed, which holds for large groups on tests of moderate difficulty.
On an easy test with a hundred-point ceiling the distribution is skewed, and percentiles near the top run high.

FAQs

What is a percentile?

The share of participants who scored below you. An 86th percentile means 86 percent did worse.

What does the z-score show?

How many standard deviations the result sits from the mean. Zero is exactly average, one is about the 84th percentile, two is the 98th.

Where do I get the mean and deviation?

From the official examination statistics: organisers normally publish the mean score and the distribution after each year.

Why does the percentile differ from percent correct?

They are entirely different measures. Percent correct describes your work; a percentile describes your position among everyone else's.

Worked example

An above-average result

Input: 78 points against a mean of 65 and a deviation of 12

Output: 86th percentile at z = 1.08

Note: One standard deviation above the mean is roughly the 84th percentile, and this sits a little higher. In a group of a hundred, the score beats eighty-six of them.

Useful links

All tools in Study

Test Score Percentile Calculator

Result

Related tools

Z-score Calculator

Standard Deviation Calculator

Grade Scale Converter

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