What is the Z Score Calculator?
Calculate z-scores (standard scores) online for free. Convert a raw score to a z-score with z = (x − μ) ÷ σ, or convert a z-score back to a raw value with x = μ + zσ. Each result includes percentile, interpretation, and step-by-step work. Runs entirely in your browser with no signup.
How to use the Z Score Calculator
- Choose Raw score → Z-score or Z-score → Raw score.
- Enter the mean (μ) and standard deviation (σ).
- Enter the raw score or z-score depending on mode.
- Click Calculate.
- Copy the z-score, percentile, or full summary.
Common use cases
- Converting an IQ of 115 (μ=100, σ=15) to z = 1
- Finding the raw score at z = 1.96 for a standardized test
- Comparing test results across different scales
Frequently asked questions
- What is a z-score?
- A z-score (standard score) measures how many standard deviations a value is from the mean: z = (x − μ) ÷ σ.
- What does the percentile mean?
- It is the percentage of values below your score in a normal distribution with the given mean and SD, computed via the standard normal CDF.
- Should I use population or sample SD?
- Use the population standard deviation σ when standardizing against a known population. For sample data, compute σ from your data first (e.g. with the Statistics Calculator).
- What is z = 1.96?
- z = 1.96 corresponds to roughly the 97.5th percentile — the common cutoff for a 95% two-tailed confidence interval.
