Z-Score Grade Calculator Formula

Understand the math behind the z-score grade calculator. Each variable explained with a worked example.

Use the Z-Score Grade Calculator

Formulas Used

Z-Score

z_score = (score - mean) / std_dev

Points Above Mean

points_above = score - mean

Standard Deviations from Mean

std_devs_away = (score - mean) / std_dev

Variables

VariableDescriptionDefault
scoreYour Score85
meanClass Mean75
std_devStandard Deviation10

How It Works

How to Calculate a Z-Score

A z-score measures how many standard deviations a score is from the mean.

Formula

Z = (Score - Mean) / Standard Deviation

  • Z = 0 means you scored at the average
  • Z > 0 means above average
  • Z < 0 means below average

    • Worked Example

    A student scores 85 in a class with mean 75 and standard deviation 10.

    score = 85mean = 75std_dev = 10
    1. 01Z-score = (85 - 75) / 10 = 1.0
    2. 02Points above mean = 85 - 75 = 10
    3. 03The student is 1.0 standard deviations above the mean.

    Frequently Asked Questions

    What is a good z-score?

    A z-score of 1.0 or higher means you are above average. A z-score of 2.0+ means you are in roughly the top 2.5% of the class.

    Can a z-score be negative?

    Yes, a negative z-score means your score is below the class average.

    How does z-score relate to percentile?

    A z-score of 0 is the 50th percentile, 1.0 is about the 84th percentile, and 2.0 is about the 97.7th percentile.

    Ready to run the numbers?

    Open Z-Score Grade Calculator