Z-Score Calculator

Calculate z-scores for standard normal distribution. Enter your raw value, mean, and standard deviation to determine how many standard deviations your value is from the mean, along with its corresponding percentile.

What is a Z-Score?

A z-score (also called a standard score) measures how many standard deviations a data point is from the mean of a distribution. It's calculated using the formula: z = (X - μ) / σ, where X is the raw value, μ is the mean, and σ is the standard deviation.

How to Use This Calculator

1. Enter your raw value (X) - the data point you want to analyze
2. Enter the mean (μ) of your dataset
3. Enter the standard deviation (σ) of your dataset
4. Click "Calculate Z-Score" to see your results

Interpreting Your Results

• Z-Score: Positive values indicate the data point is above the mean, negative values indicate it's below the mean
• Percentile: Shows the percentage of data points that fall below your value in a normal distribution
• A z-score of 0 means the value equals the mean
• About 68% of values fall within ±1 standard deviation (z-score between -1 and 1)
• About 95% of values fall within ±2 standard deviations
• About 99.7% of values fall within ±3 standard deviations

Common Applications

Z-scores are widely used in statistics, research, and data analysis for:

• Standardizing test scores (SAT, IQ tests, etc.)
• Identifying outliers in datasets
• Comparing values from different normal distributions
• Quality control in manufacturing
• Financial analysis and risk assessment