# Margin of Error Calculator Calculate the margin of error for a mean or proportion from sample size, confidence level, and variability > Canonical page: https://elysiatools.com/en/tools/margin-of-error-calculator - **Category:** Math & Numbers - **Keywords:** margin of error, confidence level, sample size, standard error, survey proportion, calculator ## Overview The Margin of Error Calculator helps researchers, statisticians, and analysts determine the margin of error for a sample mean or proportion. By inputting your sample size, confidence level, and standard deviation or population proportion, you can instantly calculate the standard error, critical value, and margin of error to evaluate the reliability and precision of your survey or experiment results. ## Inputs - **Estimate Type** (select) - **Standard Deviation** (number) - **Sample Size** (number) - **Confidence Level** (select) - **Population Proportion** (number) - **Proportion Scale** (select) - **Use t Critical Value for Mean** (checkbox) - **Decimal Places** (number) ## When to use - Analyzing survey results to determine the accuracy of a population proportion estimate. - Calculating the margin of error for a sample mean in scientific or academic research. - Determining the reliability of A/B test metrics or market research data before making business decisions. ## How it works - Select your estimate type (Mean or Proportion) and set your desired confidence level (e.g., 90%, 95%, 99%). - Enter the sample size and either the standard deviation (for means) or the population proportion (for proportions). - Choose whether to use the t-distribution critical value for means and adjust the decimal places for your output. - The calculator instantly outputs the margin of error, standard error, and critical value in a structured JSON format. ## Use cases - Political pollsters estimating the true voter support percentage from a sample survey. - Quality control inspectors calculating the acceptable variance in product weights or dimensions. - Market researchers determining the reliability of customer satisfaction scores. ## Frequently asked questions ### What is a margin of error? The margin of error represents the range of values below and above the sample statistic in a confidence interval. It indicates how much the sample results might differ from the true population. ### Should I use the mean or proportion estimate type? Use 'Mean' when analyzing continuous data like height, weight, or test scores. Use 'Proportion' for categorical data, such as the percentage of people who answered 'yes' to a survey question. ### When should I use the t-distribution? The t-distribution is generally recommended when calculating the margin of error for a mean, especially if the population standard deviation is unknown or the sample size is small. ### How does sample size affect the margin of error? Increasing the sample size decreases the margin of error, leading to a more precise estimate of the population parameter. ### What confidence level should I choose? A 95% confidence level is the standard for most scientific and market research, meaning you can be 95% confident that the true population parameter falls within your calculated margin of error. ## Related tools - [Duct Size Calculator (Flow Rate × Velocity)](https://elysiatools.com/en/tools/duct-size-calculator): Size a duct cross-section from the air flow rate Q and the design mean velocity v: area A = Q/v. Circular duct diameter D = √(4A/π). Rectangular duct with aspect ratio r = a/b gives b = √(A/r) and a = r·b, plus the ASHRAE equivalent diameter D_eq = 1.30·(a·b)^0.625/(a+b)^0.25. 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