# Standard Normal Calculator Calculate standard normal PDF, CDF, tail probability, two-tail probability, and central area from a z-score > Canonical page: https://elysiatools.com/en/tools/standard-normal-calculator - **Category:** Math & Numbers - **Keywords:** standard normal, z score, normal cdf, tail probability, statistics ## Overview Calculate probabilities for the standard normal distribution. Enter a z-score to get density, cumulative probability, right-tail area, two-tail area, and central area. This is useful for z-tests, percentiles, and confidence-interval interpretation. ## Inputs - **Z Score** (number): e.g. 1.96 - **Probability Mode** (select) - **Decimal Places** (number) ## When to use - Conducting hypothesis testing using z-tests to find exact p-values. - Determining confidence intervals and central probability areas for statistical analysis. - Calculating percentiles and cumulative probabilities for normally distributed data. ## How it works - Enter your calculated z-score into the primary input field. - Select your desired probability mode, such as left-tail, right-tail, two-tail, or central area. - Adjust the decimal places setting to match your required level of precision. - The calculator instantly processes the z-score and outputs the exact probabilities in a structured format. ## Use cases - Finding exact p-values for statistical hypothesis testing and z-tests. - Determining the proportion of a population that falls above or below a specific threshold. - Verifying critical values and confidence levels for academic research or data science projects. ## Frequently asked questions ### What is a z-score? A z-score represents the number of standard deviations a data point is from the mean of a standard normal distribution. ### What does the left-tail probability mean? The left-tail probability, or cumulative distribution function (CDF), shows the probability that a value is less than or equal to your given z-score. ### How do I find the p-value for a two-tailed test? Enter your z-score and look at the two-tail probability output. This represents the area in both tails beyond the absolute value of your z-score. ### Can I adjust the precision of the results? Yes, you can use the decimal places setting to round the calculated probabilities to your preferred number of digits, up to 10 decimal places. ### What is the central probability? The central probability is the area under the normal curve between the negative and positive values of your z-score, often used for confidence intervals. ## Related tools - [Chi-Square Distribution Calculator](https://elysiatools.com/en/tools/chi-square-distribution-calculator): Calculate chi-square distribution PDF, CDF, and right-tail probability from a statistic and degrees of freedom - [Exponential Distribution Calculator](https://elysiatools.com/en/tools/exponential-distribution-calculator): Calculate PDF, CDF, survival probability, and interval probability for an exponential distribution - [Fitness Workout PDF Generator](https://elysiatools.com/en/tools/fitness-workout-pdf-generator): Generate a printable workout-plan PDF from JSON or CSV data with exercise tables, progress boxes, and optional QR video links - [PDF Extract Selected Pages](https://elysiatools.com/en/tools/pdf-extract-selected-pages): Extract selected pages from one PDF and generate a new PDF - [PDF Form Data Export](https://elysiatools.com/en/tools/pdf-form-data-export): Read AcroForm field names, types and current values from a PDF and export them to JSON - [PDF Formula Extractor (LaTeX / MathML / MathJax) with AMS Equation-Number Preservation](https://elysiatools.com/en/tools/pdf-latex-mathml-mathjax-formula-extractor-and-equation-number-preserver): Detect and reconstruct embedded math formulas from vector PDFs: math-font recognition (CMMI/CMSY/CMEX, STIX, Cambria Math), Unicode math, super/subscripts and stacked fractions, AMS equation numbers ((2a)/(2b) subequations) preserved; outputs copyable LaTeX, presentation MathML (MathJax/KaTeX-compatible) and a downloadable .tex bundle. - [PDF to JSON Structure Explorer](https://elysiatools.com/en/tools/pdf-to-json-structure-explorer): Extract structured OpenDataLoader JSON from a PDF and browse headings, paragraphs, tables, lists, pages, and bounding boxes in an explorer view - [T Distribution Calculator](https://elysiatools.com/en/tools/t-distribution-calculator): Calculate Student t distribution PDF, CDF, tail probability, two-tail probability, and central area ## Samples - [Web Image Processing Python Samples](https://elysiatools.com/en/samples/web-image-processing-python): Web Python image processing examples using PIL/Pillow including reading, saving, resizing, and format conversion - [PDF Samples](https://elysiatools.com/en/samples/pdf-samples): Generated PDF samples from tools dated 2026-02-01 to 2026-02-10 - [Android Image Processing Java Samples](https://elysiatools.com/en/samples/android-image-processing-java): Android Java image processing examples including reading/saving images, scaling, and format conversion - [Android Image Processing Kotlin Samples](https://elysiatools.com/en/samples/android-image-processing-kotlin): Android Kotlin image processing examples including reading/saving images, scaling, and format conversion