DIY Cost Tools
Standard Deviation Calculator
MATH CALCULATOR
Find the mean, variance, population standard deviation, and sample standard deviation for a list of numbers.
How it works
Paste a list of numeric observations. The calculator computes the average and squared distances from that average, then reports both population and sample measures.
Formula
Population variance = Σ(x − mean)² ÷ N. Sample variance = Σ(x − mean)² ÷ (N − 1). Standard deviation is the square root of variance.
Worked example
For 4, 8, 6, 5, 3, and 7, the mean is 5.5; population standard deviation is about 1.7078 and sample standard deviation is about 1.8708.
Important limits
- Choose the population result only when the list represents the entire population of interest.
- The sample formula requires at least two observations.
- Outliers and nonrepresentative samples can make a summary misleading.
Frequently asked questions
Why are there two standard deviations?
The sample result uses N − 1 to estimate population variability from a sample; the population result uses N.
Can I paste line-separated data?
Yes. Commas, spaces, semicolons, and line breaks are accepted.
Sources and review notes
Formulas follow standard definitions used in statistical practice, including the sample variance correction for estimating a population from sample data. Last reviewed September 29, 2026.