Everything runs locally. Your numbers are parsed in the browser, z and the normal-curve probabilities are computed on the page, and nothing is uploaded or stored. Change any field and the result updates instantly; it works offline once loaded.
Free Z-Score Calculator
Runs entirely in your browser - no upload, no sign-up.
Inputs
Enter the value, the population mean, and the standard deviation. The z-score updates as you type.
Z-score1.5Typical · Above the mean
Percentile93.32%Share of values below x
93.32%P(X < x)
6.68%P(X > x)
13.36%Two-tailed p
93.32Percentile rank
Interpretation85 is 1.5 standard deviations above the mean, higher than about 93.32% of the distribution.
What is a z-score?
A z-score, or standard score, tells you how many standard deviations a value sits above or below the mean: z = (x − mean) / standard deviation. This free calculator returns z from your raw value, mean and standard deviation, plus its percentile and the normal-distribution probabilities - all in your browser.
How to use
- 1Enter the raw score. Type the value you want to standardize into the raw score (x) box.
- 2Enter the mean and standard deviation. Add the distribution's mean (μ) and standard deviation (σ). The standard deviation must be greater than 0.
- 3Read the result. The z-score appears with a plain-language reading, alongside its percentile, the cumulative and upper-tail probabilities, and the two-tailed p-value. Use Copy results to grab them all.
Who it's for
- Students converting an exam mark or lab measurement into a standard score for a statistics assignment without opening a z-table.
- Researchers and analysts standardizing values, flagging outliers, and reading the percentile or p-value straight off the score.
- Teachers showing a class how the same raw score maps to different z-scores and percentiles as the mean and spread change.
- Quality and finance folks checking how far a data point sits from the average in standard-deviation units before acting on it.
- Anyone comparing scores on different scales - a z-score puts an SAT mark and a class test on the same footing.
FAQ
Is the z-score calculator free?
Yes - 100% free, no sign-up, and no limits. The whole calculation runs in your browser and your numbers are never uploaded.
How do you calculate a z-score?
Subtract the mean from your value, then divide by the standard deviation: z = (x − μ) / σ. A z of +1.5 means the value is 1.5 standard deviations above the mean; a negative z means it is below the mean.
How do I turn a z-score into a percentile?
The percentile is the area under the standard normal curve to the left of z, written Φ(z). This tool computes it for you: a z of 0 is the 50th percentile, +1 is about the 84th, +1.96 about the 97.5th. It uses a high-accuracy approximation of the normal CDF that matches a printed z-table to four decimals.
What is a good or normal z-score?
There is no single 'good' z-score - it depends on context. As a rough guide, about 95% of values in a normal distribution fall between z = −2 and +2, so |z| under 2 is typical, 2 to 3 is unusual, and 3 or more is extreme. A higher z is only 'better' when a higher raw value is better.
What is the two-tailed p-value shown here?
It is P(|Z| > |z|) = 2 × (1 − Φ(|z|)), the probability of seeing a value at least this far from the mean in either direction. For z = ±1.96 it is about 0.05, which is why 1.96 is the classic cutoff for a 95% confidence level.
What is the difference between a z-score and a t-score?
A z-score uses the known population standard deviation and the normal distribution. A t-score is used when the standard deviation is estimated from a small sample; it follows the heavier-tailed t-distribution. For large samples the two nearly coincide. This calculator computes the z-score.
Can a z-score be negative or greater than 3?
Yes. A negative z-score simply means the value is below the mean. Z-scores are unbounded, so values far from the mean can exceed +3 or drop below −3, though in a normal distribution fewer than about 0.3% of values do.