Formula and calculation method
z = (observation − mean)/standard deviation. Percentile uses the standard normal distribution.
Use consistent units for all comparable inputs. The displayed result is rounded; arithmetic is performed with the full available numeric precision. Check your source measurements before relying on the result.
How to use z-score calculator
- Set Observation. The example below uses 85.
- Set Population mean. The example below uses 70.
- Set Population standard deviation. The example below uses 10.
- Select Calculate to update the result. Reset restores the illustrated inputs. Copy, print or download your own result if you need a record.
Worked example
Example inputs
- Observation
- 85
- Population mean
- 70
- Population standard deviation
- 10
- Z score
- 1.5
- Normal percentile (%)
- 93.31927987
Factors affecting your result
Use consistent units for all comparable inputs. The displayed result is rounded; arithmetic is performed with the full available numeric precision. Check your source measurements before relying on the result.
Changing observation changes the scenario being evaluated. Adjust one input at a time when comparing results, keep a copy of the assumptions, and compare values using the same unit and period. A precise arithmetic result does not make an uncertain assumption precise.
Frequently asked questions
How does the z-score calculator work?
z = (observation − mean)/standard deviation. Percentile uses the standard normal distribution.
What inputs does Z-Score Calculator need?
Enter observation, population mean, population standard deviation. Choose values that correspond to the same situation and measurement convention.
How should I interpret the z-score calculator result?
Use consistent units for all comparable inputs. The displayed result is rounded; arithmetic is performed with the full available numeric precision. Check your source measurements before relying on the result.
Are my z-score calculator inputs uploaded?
No. The calculation runs in this browser. Favorites, recent tool names, theme and formatting preferences may be saved locally, but calculation inputs are not sent to a calculation server or stored by this website. Shared links do not include entered values.
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