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Z-Score Calculator — result sheet
Express an observation's distance from a mean in standard-deviation units.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: z = (observed value - mean) / standard deviation.
Subtracting the mean centers the observation and dividing by standard deviation makes the result unitless. A z-score of 1.5 is one and a half standard deviations above the mean; a negative score lies below it. Converting this score to a percentile would require a distributional model not assumed here.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Observed value — minimum -1000000000000; maximum 1000000000000
- Mean — minimum -1000000000000; maximum 1000000000000
- Standard deviation — Must be positive and use the same units as the observed value.; minimum 1.0E-6; maximum 1000000000000
Worked example
| Input | Value |
|---|---|
| Observed value | 85 |
| Mean | 70 |
| Standard deviation | 10 |
1.5
Assumptions and limits
- The observation, mean, and standard deviation refer to the same measure and units.
- Standard deviation must be strictly positive.
- Normality is not required to compute a z-score; no normal percentile or p-value is inferred.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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