Calculating your z-score is straightforward once you know the Z-Score formula and what each input means. This guide explains the method in plain language, walks through a manual calculation, and gives worked examples you can follow — then you can do it instantly with the Z-Score Calculator.
What is Z-Score?
The Z-Score calculation tells you your z-score from a few simple inputs. The figure you are solving for here is the z-score.
The Z-Score formula
The core formula is:
Z-score = (Value (x) - Mean (μ)) ÷ Standard deviation (σ)Here is what each input means:
- Value (x) — a number. Example: 85.
- Mean (μ) — a number. Example: 70.
- Standard deviation (σ) — a number. Example: 10.
How to calculate it step by step
- Write down the value (x) (for example, 85).
- Write down the mean (μ) (for example, 70).
- Write down the standard deviation (σ) (for example, 10).
- Apply the formula above to get your z-score.
- Double-check the result with the Z-Score Calculator.
Worked examples
Example 1
| Input / Output | Value |
|---|---|
| Value (x) | 85 |
| Mean (μ) | 70 |
| Standard deviation (σ) | 10 |
| Z-score | 1.5000 |
With value (x) of 85, mean (μ) of 70 and standard deviation (σ) of 10, the z-score works out to 1.5000.
Example 2
With value (x) of 170, mean (μ) of 70 and standard deviation (σ) of 10, the z-score works out to 10.0000.
| Result | Value |
|---|---|
| Z-score | 10.0000 |
Example 3
With value (x) of 43, mean (μ) of 70 and standard deviation (σ) of 10, the z-score works out to -2.7000.
| Result | Value |
|---|---|
| Z-score | -2.7000 |
Tips for an accurate result
- Keep your units consistent — mixing, say, months with years or grams with kilograms is the most common source of error.
- Round only at the very end. Rounding inputs early can shift the final answer noticeably.
- Re-run the numbers whenever an input changes, rather than estimating from an old result.
Prefer not to do the maths by hand? — the Z-Score Calculator does it instantly, for free, with the formula and a worked example built in.
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