How to Calculate Percentiles on Normal Curves

Percentiles are used to compare scores across a larger sample, such as a national college admissions test like the ACT and SAT. Your percentile tells you what percentage of people you scored higher than. For example, if you scored in the 85th percentile, you scored higher than 85 percent of test takers. To calculate the percentile, you will need to know your score, the mean and the standard deviation.

Things You'll Need

• Your score
• Mean score
• Standard deviation

Instructions

1. Subtract the mean from your score. For example, if you scored 33 and the mean is 24, you would get a difference of 9.

2. Divide the difference found in Step 1 by the standard deviation of the data to find the z-score, which is the number of standard deviations away from the mean that your score is. For example, if the standard deviation was 4.5, you would have a z-score of 2.

3. Convert the z-score to a percentile using a z-score chart or converter available online (see Resources section). When converting, be sure to use a one-sided test. For example, a z-score of 2 would be in the 98th percentile.

Tips & Warnings

• If your score is lower than the mean, make sure you do not drop the negative sign. You will get a negative z-score, which means the score will be lower than the 50th percentile.

References

• Finding Percentiles When Given Z-Scores
• Calculating Z-Score From Mean
• How to Calculate Quartiles

Resources

• Measuring Usability: Z-Score Converter