# Z-Score to Percentile Calculator Convert a z-score into normal-distribution percentile, tail probability, or central area > Canonical page: https://elysiatools.com/en/tools/z-score-to-percentile-calculator - **Category:** Math & Numbers - **Keywords:** z score to percentile, normal distribution, standard normal, percentile, tail probability ## Overview Convert a z-score into a standard normal probability. For the usual percentile interpretation, the tool returns the left-tail area: the percentage of values expected to fall at or below the given z-score. It can also return right-tail, two-tail, and central-area probabilities for hypothesis testing or distribution interpretation. ## Inputs - **Z Score** (number): e.g. 1.96 - **Probability Mode** (select) - **Decimal Places** (number) ## When to use - Interpreting standardized test scores to find the exact percentile ranking of a student or participant. - Conducting hypothesis testing in statistics to determine p-values from calculated z-statistics. - Analyzing quality control data to find the percentage of products falling within or outside specific standard deviations. ## How it works - Enter your calculated Z-Score into the primary input field (e.g., 1.96 or -1.5). - Select your desired probability mode: Left Tail Percentile, Right Tail Area, Two Tail Area, or Central Area. - Specify the number of decimal places required for your statistical precision. - The tool instantly calculates the exact area under the standard normal curve and outputs the corresponding probability. ## Use cases - Converting student z-scores into percentile ranks for academic grading and standardized test reporting. - Determining statistical significance (p-values) for A/B testing, marketing analytics, and scientific research. - Calculating defect probabilities and yield rates in Six Sigma and manufacturing quality control processes. ## Frequently asked questions ### What is a left-tail percentile? The left-tail percentile represents the percentage of values in a standard normal distribution that fall at or below a specific z-score. ### How do I find the p-value for a two-tailed test? Select the 'Two Tail Area' probability mode and enter your z-score. The tool will calculate the combined probability in both tails of the distribution. ### What does a z-score of 0 mean? A z-score of 0 represents the exact mean of a normal distribution, which corresponds to the 50th percentile (or a 0.5 left-tail probability). ### Can I calculate the probability of a value falling between two z-scores? While this tool calculates single z-score areas, you can find the area between two z-scores by calculating their left-tail probabilities separately and subtracting the smaller from the larger. ### How accurate are the calculations? 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