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Z Score Calculator

Calculate z-scores and normal distribution probabilities from raw scores, mean and standard deviation, with percentile conversion

Calculator Interface

Interactive calculator will be available soon

Features

  • One-click z-score from raw score, mean and standard deviation
  • Convert z-scores to percentiles, probabilities and one/two-tailed intervals
  • Built-in standard normal table — no lookup needed
  • Batch data calculation with result export
  • 100% local calculation — no uploads, ideal for students and researchers

How to Use

  1. Enter the raw score (X)
  2. Enter the population mean (μ) and standard deviation (σ)
  3. Choose the result type (z-score/percentile/probability)
  4. Click calculate to view the result and normal distribution explanation

FAQ

What is Z Score Calculator?

An online statistics tool. It calculates z-scores from raw scores, mean and standard deviation, and converts them to percentiles and normal distribution probabilities. Input: your raw score, mean and standard deviation. Output: z-score, percentile and probability results with one-click copy. Everything runs in your browser.

What is a z-score?

A z-score (standard score) measures how many standard deviations a data point is from the mean: Z=(X-μ)/σ. Z=0 means equal to the mean, Z>0 means above it, Z<0 means below it — enabling comparison across different distributions.

How do z-scores convert to percentiles?

A z-score corresponds to the cumulative probability under the standard normal curve; cumulative probability ×100% is the percentile. For example Z=1.96 ≈ 97.5th percentile, Z=0 = 50th percentile. The tool does this automatically.

What assumptions are required?

Z-score calculation assumes the data is normally distributed (or approximately so). You only need the raw score, population mean and standard deviation; you can also reverse-calculate a raw score from a known z-score.

What is the difference between one-tailed and two-tailed probabilities?

One-tailed probability computes the chance of a value above (or below) a threshold; two-tailed probability computes the chance of falling outside ±Z, commonly used as the p-value in hypothesis testing.

Can I save the calculation results?

Yes. Results can be copied with one click, and batch calculations can be exported as CSV for homework, papers or lab reports.