Z-Score Calculator
Calculate z-scores, find percentiles, and visualize standard deviations with bell curve visualization.
Results
Enter values and click Calculate to see the result.
Theory & Formula
What is a Z-Score?
A z-score (or standard score) measures how many standard deviations a value is from the mean. It allows comparison of values from different normal distributions.
Formula
\(z = \frac{X - \mu}{\sigma}\)
Where: X = raw score, μ = population mean, σ = standard deviation
Interpretation
• Positive z-score: Value is above the mean
• Negative z-score: Value is below the mean
• z = 0: Value equals the mean
Empirical Rule (68-95-99.7)
• 68% of data falls within ±1σ (z between -1 and 1)
• 95% of data falls within ±2σ (z between -2 and 2)
• 99.7% of data falls within ±3σ (z between -3 and 3)