--- title: "Z-Score Calculator - Standard Score & Percentile | CanDoYa" description: "Free z-score calculator: enter a raw value, the mean and standard deviation to get the standard score, its percentile, and the probability - instantly in your browser." url: https://candoya.com/tools/z-score-calculator/ locale: en type: browser-tool --- # Free Z-Score Calculator Category: Calculators ## 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. 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. ## How to use it 1. **Enter the raw score** - Type the value you want to standardize into the raw score (x) box. 2. **Enter the mean and standard deviation** - Add the distribution's mean (μ) and standard deviation (σ). The standard deviation must be greater than 0. 3. **Read 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. ## Expert note The percentile and probabilities here assume the data follows a normal (bell) distribution - the z-score itself is always just (x − mean) / sd, but reading a percentile off it is only meaningful when the distribution is roughly normal. This tool treats the mean and standard deviation you enter as population parameters, so it uses the standard-normal Z rather than a t-distribution; for a small sample where you estimated σ from the data, a t-score is often the more honest choice. ## Frequently asked questions ### 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. ## Related tools - [Correlation Coefficient Calculator](https://candoya.com/tools/correlation-coefficient/) - [Standard Deviation Calculator](https://candoya.com/tools/standard-deviation-calculator/) - [Variance Calculator](https://candoya.com/tools/variance-calculator/) - [Mean, Median & Mode Calculator](https://candoya.com/tools/mean-average-calculator/) --- *Markdown edition of , published for AI agents and other automated readers. Index of key pages: .*