Z-Score Calculator — How to Calculate a Standard Score
Convert a raw score to a z-score with z = (x − mean) / SD. Example: x = 85, mean = 70, SD = 10 → z = 1.5. States the linear scaling assumption and SD > 0. Runs in your browser for coursework and quick checks.
How it works
Enter a raw score, the distribution mean, and the standard deviation. The tool returns z = (x − mean) / SD so you can see how many SDs the score sits above or below the mean. Runs in your browser for coursework.
Formula and assumptions
z = (x − μ) / σ. Keep these limits in mind:
- SD (σ) must be positive; zero or negative SD is rejected.
- This is a linear rescaling of x relative to the given mean and SD, not a full normality test.
- Units cancel: z is dimensionless.
- Pair with a p-value page if you next need a normal-tail probability from z.
Example
Example: x = 85, mean = 70, SD = 10 → z = (85 − 70) / 10 = 1.5.
When to use it
- Homework: convert a test score to a standard score.
- Compare two scores from distributions with different means or spreads.
- Prepare a z to feed into a two-tailed p-value check.
Frequently asked questions
What does z = 1.5 mean?
The raw score is 1.5 standard deviations above the stated mean.
Can SD be zero?
No. Division by zero is undefined; enter SD > 0.
Is a large |z| always “significant”?
Not by itself. Significance needs a model and a p-value or critical value, not only the z number.
Does this assume a normal distribution?
The algebra of z does not require normality, but many follow-on uses (like normal p-values) do.
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Questions or feedback
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