How to use the Z-score Calculator
Estimate z-score from raw value (x), mean (μ), standard deviation (σ) with the Z-score Calculator. It includes Find the Z-score, Find the raw value workflows, so choose the one that matches the values you actually know. Use it to check the arithmetic while keeping the displayed method and entered values with your work.
Step by step
- For the Z-score example, select Find the Z-score and enter raw value (x), mean (μ), standard deviation (σ). Keep each value in the unit displayed beside its field.
- Review the selected Z-score workflow and inputs, then read z-score in the result panel.
- Change one Z-score assumption at a time to compare scenarios. Use Reset to restore this tool's worked example values.
How the calculation works
Converts bidirectionally with z = (x − μ) / σ and x = μ + zσ.
Worked example
To reproduce the Z-score worked example, reset the calculator. Select the Find the Z-score workflow. Use raw value (x) 85; mean (μ) 70; standard deviation (σ) 10. The result is z-score of 1.5. Find the Z-score: Converts bidirectionally with z = (x − μ) / σ and x = μ + zσ. Review the displayed units before comparing the result.
Understanding the result
The Z-score reports z-score. Use it to check the arithmetic while keeping the displayed method and entered values with your work. The result depends on the entered values, selected mode, and displayed mathematical assumptions.
How to check the answer
Check the Z-score answer by substituting z-score back into the stated relationship. Test a simple value such as zero, one, or an equal pair, then confirm that sign, scale, units, and rounding match Converts bidirectionally with z = (x − μ) / σ and x = μ + zσ.
Common questions
What does the Z-score calculate?
Estimate z-score from raw value (x), mean (μ), standard deviation (σ) with the Z-score Calculator.
Which inputs does the Z-score example use?
The worked example uses raw value (x), mean (μ), standard deviation (σ) in the Find the Z-score workflow. Other workflows can show different fields. Keep the chosen workflow and units with the result when comparing calculations.
Is the Z-score result exact?
The result depends on the entered values, selected mode, and displayed mathematical assumptions. Recheck raw value (x), mean (μ), standard deviation (σ) and use z-score only for a decision where that level of precision is appropriate.