Standard Score Calculator
Calculate the z-score (standard score) of a value given the mean and standard deviation of a dataset.
Published by:
isCalculator Editorial Team
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How to use this tool?
How to Use the Standard Score (Z-Score) Calculator
This calculator computes the z-score, which tells you how many standard deviations a raw score is from the mean.
- Enter the Raw Score (X) — the individual data point you want to standardize (e.g., 85).
- Enter the Mean (μ) — the average of the dataset (e.g., 70).
- Enter the Standard Deviation (σ) — must be a positive number (e.g., 10).
- Click Calculate Z-Score.
Result: The z-score is displayed along with its interpretation (above, below, or exactly at the mean). The formula used is:
z = (X - μ) / σ
Note: All inputs accept decimal numbers. Standard deviation must be greater than zero.
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Frequently Asked Questions
A standard score (z-score) indicates how many standard deviations an element is from the mean of a dataset. It is calculated as z = (X - μ) / σ.
A negative z-score means the raw score is below the mean. For example, a z-score of -1.5 indicates the value is 1.5 standard deviations below the mean.
No, standard deviation must be greater than zero for a valid z-score calculation. If all values are identical, the standard deviation is zero and the z-score is undefined.
