Standard Deviation Calculator

Standard Deviation Calculator measures how spread out a list of numbers is. It calculates population or sample standard deviation and variance together with the count, mean, median, minimum, maximum, range and sum, using Welford’s numerically stable method with a corrected second pass. Invalid entries are reported by position instead of being skipped.

Standard deviation is the most common measure of variability, used for test scores, measurements, quality control, finance and research. Choosing the right formula and getting a precise result matters, and a calculator that flags typos prevents a single bad entry from distorting the answer.

1. Paste or type your numbers, separated by commas, spaces or new lines.
2. Choose Population if the list is the whole group, or Sample if it is a sample from a larger group.
3. Press Calculate statistics (or Ctrl/Cmd + Enter).
4. Fix any entries listed as invalid or blank, then calculate again.
5. Read the results, then copy the summary or download it as CSV or text.

• Population (÷ n) and sample (÷ n − 1) standard deviation and variance
• Count, mean, median, minimum, maximum, range and sum
• Welford’s method, a corrected second pass and compensated summation for accurate results
• Decimals, negative numbers and scientific notation
• Invalid and blank entries identified by position — never silently ignored
• Up to 100,000 values; CSV export with every value and statistic

• Use Sample when you are estimating the spread of a larger population from part of it.
• Check the minimum and maximum for typos — an extra digit stands out immediately.
• Compare the mean and median: a large gap suggests skewed data or outliers.
• Report the standard deviation with the same units as your data.