Standard Deviation Calculator
Paste or type your numbers to compare sample and population standard deviation side by side, with the mean and related summary values shown alongside them.
Compare sample and population spread
Enter your values, or try an example.
Your results and calculation will appear here.
Show calculation
How to use this calculator
- Paste or type values separated by commas, spaces, tabs or new lines.
- Calculate to see sample and population results together.
- Use the population result for the full group, or the sample result when estimating a wider population.
Worked example: test scores
data: 72, 78, 81, 85, 94
Sample standard deviation = 8.2158; Population standard deviation = 7.3485
The sample standard deviation is 8.2158, in the same units as your data. The population standard deviation is 7.3485, in the same units as your data.
Example calculation
- n = 5; sum = 410; mean = sum / n = 82.
- Squared-deviation sum Σ(x − mean)² = 270.
- Population variance = 270 / 5 = 54; population SD = √variance = 7.3485.
- Sample variance = 270 / 4 = 67.5; sample SD = 8.2158.
Formula & assumptions
Population SD = √[Σ(xᵢ − x̄)² / n]; sample SD = √[Σ(xᵢ − x̄)² / (n − 1)].
- Every entered observation has equal weight; repeat notation expands observations.
- Sample standard deviation needs at least two values.
- Standard deviation describes spread in the original units; it does not prove a normal distribution.
Sources
Reviewed: October 2026
Common questions
What is the difference between sample and population standard deviation?
Population SD divides squared deviations by n. Sample SD divides by n − 1, correcting the variance estimate when estimating population spread from a sample.
Can I find standard deviation from the mean alone?
No. A mean does not describe the spread. You need observations or additional information about their deviations.
Use these tools for mathematical information, not as a substitute for checking assumptions. Read our methodology or disclaimer.