# Percentile to Z-Score Calculator Convert a normal percentile, tail area, or central area into a standard normal z-score > Canonical page: https://elysiatools.com/en/tools/percentile-to-z-score-calculator - **Category:** Math & Numbers - **Keywords:** percentile to z score, inverse normal, standard normal, quantile, statistics ## Overview Convert a normal-distribution probability into a z-score. For the usual percentile interpretation, enter a left-tail percentile such as 95 to get the z-score where 95% of the standard normal distribution lies below it. Right-tail and central-area modes are also included for confidence intervals and hypothesis-testing workflows. ## Inputs - **Percentile** (number): e.g. 95 - **Input Scale** (select) - **Probability Mode** (select) - **Decimal Places** (number) ## When to use - Finding the critical z-value for a specific confidence interval in hypothesis testing. - Converting standardized test percentiles back into raw z-scores for comparative analysis. - Determining the exact standard deviations from the mean for a given probability area. ## How it works - Enter your target probability or percentile value into the calculator. - Select the input scale (percent or proportion) and the probability mode (left-tail, right-tail, or central area). - Specify the number of decimal places required for your final result. - The tool applies the inverse standard normal cumulative distribution function to output the precise z-score. ## Use cases - Calculating critical values for z-tests and confidence intervals in academic research. - Mapping student percentile ranks to standard normal scores in psychometrics and educational testing. - Setting quality control thresholds in manufacturing based on acceptable defect probabilities. ## Frequently asked questions ### What is the difference between left-tail and right-tail modes? Left-tail mode calculates the z-score where the given percentage falls below the value, which is the standard definition of a percentile. Right-tail mode calculates the z-score where the percentage falls above the value. ### How do I calculate a z-score for a 95% confidence interval? Select the 'Central Area' probability mode and enter 95 as a percent. The calculator will output the critical z-score (approximately 1.96) that bounds the middle 95% of the distribution. ### Can I input proportions instead of percentages? Yes, simply change the Input Scale setting from 'Percent' to 'Proportion' and enter a decimal value between 0 and 1 (e.g., 0.95 instead of 95). ### What formula does this calculator use? It uses the inverse cumulative distribution function, also known as the quantile function or probit function, for the standard normal distribution. ### How many decimal places can I generate? 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