Z-Score Calculator
How many standard deviations a value sits from the mean.
Results
Z-score
1.625000
Difference
13.000000
Value
81.000000
What this tool does
A z-score turns any measurement into a common scale, so a test mark and a machine reading can be compared directly. In a normal distribution about 68 % of values fall between −1 and 1, and 95 % between −2 and 2, which is why the two-sigma value is shown.
Formula
z = (x − µ) ÷ σ
Variables
| Symbol | Meaning | Unit |
|---|---|---|
x | Value | — |
m | Mean (average) | — |
s | Standard deviation | — |
Z | Z-score | — |
D | Difference | — |
V | Value | — |
Worked example
- Value78
- Mean (average)65
- Standard deviation8
- Z-score1.625000
- Difference13.000000
- Value81.000000
Limitations
- Standard deviation and variance are calculated for a sample (dividing by n − 1). For a full population, divide by n instead.
- The calculation runs at full precision and only the display is rounded. If you copy an intermediate value and retype it, small differences can appear.