Z-Score Calculator
Calculate z-scores, raw scores, probabilities, and percentiles with step-by-step solutions and normal distribution visualizations.
Calculator
Select a calculation mode and enter the required values to calculate z-scores, raw scores, or probabilities.
Z-Score
0
Probability
0
Percentile
0%
Percentage of values below this z-score
Normal Distribution
Step-by-Step Solution
Complete User Guide
Z-Score Formula
z = (X - μ) / σ
- z: Z-score (standard score)
- X: Raw score (observed value)
- μ: Mean (average)
- σ: Standard deviation
Interpretation
- z = 0: Value equals the mean
- z > 0: Value is above the mean
- z < 0: Value is below the mean
- |z| < 1: Within 1 standard deviation (68% of data)
- |z| < 2: Within 2 standard deviations (95% of data)
- |z| < 3: Within 3 standard deviations (99.7% of data)
Examples
Example 1: Calculate Z-Score
Input: X = 75, μ = 70, σ = 10
Result: z = (75 - 70) / 10 = 0.5
Example 2: Calculate Raw Score
Input: z = 1.5, μ = 70, σ = 10
Result: X = 70 + (1.5 × 10) = 85