A Z-score tells you how many standard deviations a value is from the mean. A Z-score of 0 means the value equals the mean; +1 means one SD above, -2 means two SDs below.

How do I interpret Z-scores?

In a normal distribution: ~68% of values fall within ±1 SD (Z between -1 and 1), ~95% within ±2 SD, and ~99.7% within ±3 SD.

What is a percentile?

A percentile indicates the percentage of values that fall below a given score. Z=0 corresponds to the 50th percentile (median); Z=1.645 to the 95th percentile.

When are Z-scores used?

Z-scores are used to compare values from different distributions, standardize test scores, identify outliers, and calculate probabilities in hypothesis testing.

What if Z-score is very high or low?

Z-scores beyond ±3 are rare (only 0.3% of data in a normal distribution). Values beyond ±3 are often considered potential outliers.

Z-Score Calculator

Convert between raw scores, Z-scores, and percentiles.

Calculation Mode

Raw Value (x)

The value you want to convert

Mean (μ)

Average of the distribution

Standard Deviation (σ)

Spread of the distribution

Normal Distribution

Z-Score

0

z = (85 - 75) / 10

Z-Score

Standard deviations from μ

Percentile

% below this value

Raw Value

x = μ + zσ

Interpretation

This value is 0 standard deviations above the mean. Only 0% of values are lower than this.

Documentation

Understanding Z-Scores

A Z-score standardizes values from any normal distribution to the standard normal distribution (mean=0, SD=1), allowing comparison across different scales.

Z-Score

Raw from Z

Percentile

Frequently Asked Questions

How to Use

About the Z-Score

What it calculates

This z-score solves mathematical and statistical problems using standard formulas. Calculate Z-score from raw value and vice versa.

When to use it

Use for homework, data analysis, exam prep, or quick verification of manual calculations.

Example

Adjust the inputs above to model your specific scenario with the Z-Score.

Explore More

Z-Score Calculator

Calculation Mode

Normal Distribution

0

Interpretation

Understanding Z-Scores

About the Z-Score

Related Calculators

ANOVA (One-Way)

Chi-Square

p-value

Relative Risk

T-Test

Z-Test