Standard Deviation Calculator

Standard deviation measures how spread out a set of numbers is around their average. A small standard deviation means the values cluster tightly around the mean. A large one means they are scattered widely. It is one of the most used statistics in science, finance, and engineering. The key distinction is between sample and population standard deviation. Use sample SD (divides by n−1) when your data is a subset drawn from a larger population. Use population SD (divides by n) when you have data for every member of the entire group. This calculator accepts any list of numbers, computes both standard deviations, and also returns the mean, variance, count, sum, min, and max, the full descriptive statistics summary.

• Academic research and surveys: Researchers report mean ± standard deviation for measurements. Paste the raw data to compute both values without spreadsheet software.
• Quality control in manufacturing: Production measurements should cluster around a target value. High SD signals inconsistency and prompts investigation of the process.
• Finance and portfolio risk: Daily returns with high standard deviation indicate volatile investments. Compare SD across assets to assess relative risk.
• Sports and performance analytics: Athlete performance metrics (times, scores, distances) analyzed with SD reveal consistency. A low SD means a reliable performer.

1. 1Enter numbers separated by commas in the input box.
2. 2The calculator parses the input and converts each token to a number.
3. 3It computes the mean (arithmetic average) of all values.
4. 4It finds the squared difference between each value and the mean.
5. 5Sample variance divides the sum of squared differences by n−1. Population variance divides by n.
6. 6Standard deviation is the square root of variance for each type.

• Using population SD when you have a sample: If your data is a sample from a larger population (common in surveys and experiments), use sample SD. Population SD is for when you have measurements of every member of the group.
• Including non-numeric text in the input: The parser splits on commas and converts each token to a number. Any non-numeric character (letters, extra symbols) causes an error. Remove headers, units, or labels before pasting.
• Interpreting SD without knowing the mean: A SD of 5 could be large or small depending on the mean. For data with a mean of 6, SD=5 means huge spread. For data with a mean of 500, SD=5 is very tight. Always report both.
• Confusing SD with standard error: Standard error of the mean (SEM) = SD / √n. It measures uncertainty of the mean estimate, not variability of individual data points. SD and SEM are different quantities with different interpretations.

• Use the 68-95-99.7 rule for normal data: For normally distributed data, mean ± 1 SD covers 68% of values, ± 2 SD covers 95%, and ± 3 SD covers 99.7%. This gives you a quick sense of what is typical versus unusual.
• Check for outliers using SD: Values more than 3 SDs from the mean are statistical outliers in a normal distribution. Compare your min and max against mean ± 3 × SD to spot potential data entry errors.
• Paste data from spreadsheets: Copy a column of numbers from Excel or Google Sheets and paste it here. The comma-separated format matches what most spreadsheets produce when copying a single column.
• Compare CV (coefficient of variation) across datasets: For comparing variability across datasets with different means, compute CV = (SD / mean) × 100. A dataset with mean 100 and SD 10 has CV = 10%. This calculator gives you both values to compute it.