Z-score Calculator guide
Z-score Calculator: Standard Scores and Percentiles
Use our z-score calculator to convert a value to a z-score and percentile, or find the value at a given percentile, for a normal distribution.
By the AllCalculator editorial teamUpdated 16 October 20261 min read
A z-score tells you how many standard deviations a value is from the mean. It lets you compare results from different tests and work out percentiles. Our Z-score Calculator does the maths.
How to use the calculator (Z-score Calculator)
Choose what you know:
- Value, mean and SD: get the z-score and percentile.
- The z-score: get the probabilities.
- A percentile: get the z-score and value at that percentile.
The formula
z = (x − μ) ÷ σ
- x is your value
- μ is the mean
- σ is the standard deviation
A positive z-score is above the mean and a negative one is below.
The 68-95-99.7 rule
For normally distributed data:
| Within | Share of values |
|---|---|
| 1 SD of the mean | About 68% |
| 2 SD | About 95% |
| 3 SD | About 99.7% |
A worked example
With the calculator's default settings, a test score of 85 where the mean is 70 and the standard deviation is 10:
- z = (85 − 70) ÷ 10 = 1.5
- That's the 93rd percentile: about 93% of people scored lower.
Frequently asked questions
What's a good z-score?
It depends what you're measuring. Above 2 or below −2 is unusual, happening about 5% of the time.
Does my data need to be normal?
The percentiles assume a normal (bell-shaped) distribution. The z-score itself works for any data.
How do I find the mean and SD?
Use our Statistics Calculator. For hypothesis tests, see our P-value Calculator.
Sources and further reading
- NIST/SEMATECH e-Handbook of Statistical Methodsitl.nist.gov
- Wolfram MathWorld: z-scoremathworld.wolfram.com
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This guide is general information to help you understand your options. It isn't financial, tax, legal or building advice and doesn't take your personal circumstances into account. Figures were checked when the guide was last updated and can change, so confirm anything important with GOV.UK, HMRC, a regulated adviser or a qualified tradesperson.