CalmCalc
MATH

Z-score Calculator

Estimate z-score from raw value, z-score, mean with the Z-score Calculator.

What do you want to solve?Convert either direction between a raw value and its standard score.
2 options
Z-SCORE1.5

Find the Z-score: Converts bidirectionally with z = (x − μ) / σ and x = μ + zσ.

Raw value (x)
85
Mean (μ)
70
Standard deviation (σ)
10
Z-score
1.5
Position
1.5 SD above the mean
Estimate based on the values shown
MethodConverts bidirectionally with z = (x − μ) / σ and x = μ + zσ.

Before you use the result

The result depends on the entered values, selected mode, and displayed mathematical assumptions.

Sources

CALCULATOR GUIDE

How to use the Z-score Calculator

Estimate z-score from raw value, z-score, mean 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

  1. For the Z-score, enter raw value, z-score, mean, standard deviation. Keep each value in the unit displayed beside its field.
  2. Review the selected Z-score workflow and inputs, then read z-score in the result panel.
  3. 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

In the Z-score worked example, raw value 85, z-score 1.5, mean 70, standard deviation 10 produces 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, z-score, mean with the Z-score Calculator.

Which Z-score inputs have the biggest effect?

z-score responds directly to raw value, z-score, mean, standard deviation. Change one input while holding the others constant to see its effect.

Is the Z-score result exact?

The result depends on the entered values, selected mode, and displayed mathematical assumptions. Recheck raw value, z-score, mean and use z-score only for a decision where that level of precision is appropriate.

Formula tests, limits, sources, and guide registry updated September 1, 2026.
INTERPRET THE RESULTRead the math guideCheck assumptions, limitations and comparison methods →