Z-score calculator
Enter a value, the mean, and the standard deviation to get its z-score, the percentile it falls at, and how far into the tails it sits.
z = 2.00 · 97.7th percentile
- z-score
- 2.000
- Percentile
- 97.7%
- Area below
- 97.72%
- Area above
- 2.28%
- Two-tailed p
- 4.55%
- Std devs from mean
- 2.00σ
z = (x − mean) ÷ standard deviation. Percentile and areas assume a normal distribution.
How it works
A z-score expresses how many standard deviations a value is from the mean: z = (value − mean) ÷ standard deviation. It puts any value onto a common scale, so a z of 2 always means 'two standard deviations above average', whatever the original units.
Assuming a normal distribution, the z-score maps to a percentile — the share of the distribution below the value — via the standard normal cumulative distribution. The calculator reports the area below and above, plus the two-tailed probability of a value at least this extreme in either direction.
This is the same standardization behind A/B test statistics and outlier detection. Everything is computed in your browser.
Assumptions and limitations
- Percentiles and probabilities assume the underlying data is normally distributed. For skewed or heavy-tailed data, the z-score is still defined but the percentile mapping is unreliable.
- It uses the population standard deviation you provide. If you only have a sample estimate and a small sample, a t-distribution is more appropriate than the normal.
- A z-score describes position, not importance. A large z can be trivial and a small z can matter, depending on context.
Frequently asked questions
What is a z-score?
A z-score, or standard score, is the number of standard deviations a value sits from the mean, calculated as (value − mean) ÷ standard deviation. It standardizes values so they can be compared across different scales, and underlies percentiles, outlier detection, and hypothesis testing.
How do I interpret a z-score?
A positive z is above the mean, negative is below, and the magnitude is how many standard deviations away. Under a normal distribution, about 68% of values fall within ±1, 95% within ±2, and 99.7% within ±3, so a z beyond ±2 is relatively unusual.
What is a good or bad z-score?
There is no universally good value — it depends entirely on context and on whether higher or lower is desirable. A z of +2 on a test score is excellent; a z of +2 on error rate is a problem. Interpret the sign and magnitude against what the metric means.
How does a z-score relate to a percentile?
Under a normal distribution each z-score corresponds to a percentile — the share of values below it. A z of 0 is the 50th percentile, +1 is about the 84th, and +2 is about the 98th. This calculator reports that percentile directly.
Is anything I enter stored?
No. The calculation runs entirely client-side in your browser and nothing you enter is transmitted or saved.
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