Z-Score Calculator
Calculate the z-score (standard score) for any value in a normal distribution. Find the percentile ranking and probability associated with your data point.
Inputs
Results
Z-Score
-1
How to Use This Calculator
- Enter the individual data value (X), the population mean (μ), and the population standard deviation (σ).
- The z-score is computed as z = (X − μ) / σ, measuring how many standard deviations X is from the mean.
- A z-score of 0 means X equals the mean; ±1 covers ~68% of data; ±2 covers ~95%; ±3 covers ~99.7%.
- Percentile Rank shows the percentage of values in a standard normal distribution that fall below X.
- The probability output (area under the curve) is useful for hypothesis testing and quality control (Six Sigma).
- σ must be greater than 0; negative z-scores simply indicate values below the mean.
How the result changes with Mean (μ)
| Mean (μ) | Z-Score |
|---|---|
| -800,000 | 53,339 |
| -300,000 | 20,005.6667 |
| 300,000 | -19,994.3333 |
| 800,000 | -53,327.6667 |
What each input means
- Value (x)
- The data point you want to analyze
- Mean (μ)
- The average of your dataset
- Standard Deviation (σ)
- The standard deviation of your dataset
What each result means
- Cumulative Probability
- P(X ≤ x)
- Probability Above
- P(X > x)
How this is calculated
Formula
z = (x - μ) / σEngine last updated . Checked against 1 independently-derived test — how we verify calculators.
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