# Z-Score Calculator Calculate a z-score from a raw value using a dataset or manually entered mean and standard deviation > Canonical page: https://elysiatools.com/en/tools/z-score-calculator - **Category:** Math & Numbers - **Keywords:** z score, z-score, standard score, normal distribution, statistics, percentile ## Overview Calculate a standard score for a raw value. z = (x - mean) / standard deviation Provide a dataset to derive the mean and standard deviation automatically, or enter known mean and standard deviation values directly. The result also includes the normal percentile estimate. ## Inputs - **Raw Value** (text): e.g. 85 - **Dataset Optional** (textarea): e.g. 80, 85, 90, 95, 100. If provided, mean and standard deviation are derived from this dataset. - **Mean Optional** (text): Used when dataset is empty - **Standard Deviation Optional** (text): Used when dataset is empty - **Standard Deviation Type** (select) - **Decimal Places** (number) ## When to use - Comparing individual data points from different normal distributions, such as standardized test scores. - Identifying statistical outliers within a dataset by finding values with unusually high or low standard scores. - Determining the relative standing or percentile rank of a specific value within a normal distribution. ## How it works - Enter the raw value you want to evaluate in the designated input field. - Provide a comma-separated dataset to automatically calculate the mean and standard deviation, or enter these parameters manually. - Select whether your data represents a sample or an entire population to apply the correct standard deviation formula. - The tool calculates the z-score using the formula z = (x - μ) / σ and outputs the standard score alongside the mean and standard deviation. ## Use cases - Evaluating student performance by comparing a raw exam score against the class average and spread. - Quality control in manufacturing to measure how far a product's dimensions deviate from the target specification. - Financial analysis to assess the volatility of an investment return relative to historical market performance. ## Frequently asked questions ### What is a z-score? A z-score, or standard score, indicates how many standard deviations a raw data point is above or below the mean of its distribution. ### Should I use sample or population standard deviation? Use population if your dataset includes every member of the group you are studying. Use sample if your data is only a subset of the larger population. ### What does a negative z-score mean? A negative z-score means the raw value is below the average (mean) of the dataset. A positive z-score means it is above the average. ### Can I calculate a z-score without a full dataset? Yes. If you already know the mean and standard deviation of your distribution, you can enter them manually instead of providing a full dataset. ### What is considered a normal z-score? In a normal distribution, about 68% of values have a z-score between -1 and 1, and 95% fall between -2 and 2. 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