Z-Score Calculator
Calculate the z-score (standard score) and percentile rank for any value in a normal distribution. Convert raw scores to z-scores instantly.
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How to use this calculator
z measures how many standard deviations a value x is from the mean μ. Positive z means above average; negative means below.
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Enter the raw score (x), the population mean (μ), and the standard deviation (σ).
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The z-score tells you how many standard deviations the value is from the mean.
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The percentile shows what percentage of values fall below your score in a normal distribution.
Frequently asked questions
What is a good z-score?
In a normal distribution, 68% of values fall within z = ±1, 95% within z = ±2, and 99.7% within z = ±3. A z-score of 2 means the value is in the top 2.3%.
What is z-score used for?
Z-scores are used to standardise data from different scales, identify outliers, compare observations from different distributions, and calculate probabilities in hypothesis testing.
What if my data is not normally distributed?
Z-scores can still be calculated for any dataset, but the percentile interpretation only applies to normally distributed data. For non-normal data, use empirical percentile ranks instead.
Z-Score Calculator — Standard Score & Percentile
Understanding z-scores in statistics
A z-score tells you how far a value is from the mean, measured in standard deviations. z = 0 means the value equals the mean. z = 1 means it is one standard deviation above. z = −2 means two standard deviations below. This standardisation lets you compare values from completely different scales.
Z-score and the normal distribution
In a perfectly normal distribution: 68.27% of values lie within z = ±1; 95.45% within z = ±2; 99.73% within z = ±3 (the empirical rule). The percentile from a z-score tells you what fraction of the population falls below that value.
Learn more from an authoritative source:
WikipediaT-Test Calculator
Perform a one-sample t-test to determine if a sample mean is significantly different from a known population mean. Returns t-statistic and p-value.
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Calculate the chi-square (χ²) statistic for goodness-of-fit or independence tests. Enter observed and expected frequencies to get χ² and p-value.
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Calculate the confidence interval for a population mean from sample data. Supports 90%, 95%, and 99% confidence levels.
Sample Size Calculator
Calculate the minimum sample size required for a statistically valid survey or experiment. Specify confidence level, margin of error, and population size.
Percentile Calculator
Find the percentile rank of a score in a dataset, or find the value at a given percentile. Enter up to 10 data values.
Poisson Distribution Calculator
Calculate Poisson probabilities for rare events. Find P(X = k), P(X ≤ k), and P(X > k) given an average rate λ.
Results are estimates for informational purposes only and do not constitute professional financial, medical, legal, or technical advice. Read full disclaimer →