Standard Deviation Calculator

Enter your data values and calculate the standard deviation with a complete step-by-step breakdown. Choose between population ($\sigma$) and sample ($s$) modes.

• Population standard deviation ($\sigma$) — divides by N; use when your data IS the entire population
• Sample standard deviation ($s$) — divides by $n-1$; use when your data is a sample from a larger group

How to Use This Calculator

1. Choose your mode — population or sample (when in doubt, use sample)
2. Enter your data as comma-separated numbers (e.g., 4, 8, 6, 5, 7)
3. See the result with count, mean, variance, and standard deviation
4. Review the steps — see each deviation, squared deviation, and the final calculation

Population vs Sample — Which Should I Use?

• Population ($\sigma$): Use when you have data for every member of the group (e.g., all 30 students in a class, all 12 months of the year)
• Sample ($s$): Use when your data is a subset of a larger group (e.g., 50 patients out of 5,000, a week of measurements representing a full year). The $n-1$ correction compensates for the fact that a sample tends to underestimate the true variability.

When in doubt, use sample — it is the safer choice and the more common one in practice.

Related

Want to understand the math behind these calculations? Read our Range and Standard Deviation tutorial for a complete explanation with worked examples and practice problems.