Standard Deviation Calculator

Calculate population and sample standard deviation with detailed statistical analysis

Population Standard Deviation

0 Ļƒ (sigma)
0 Mean (Ī¼)
0 Variance (ĻƒĀ²)
Count: 0
Sum: 0
Sum of Squares: 0

Sample Standard Deviation

0 s
0 Mean (xĢ„)
0 Variance (sĀ²)
Count: 0
Sum: 0
Degrees of Freedom: 0

How to Use the Standard Deviation Calculator

Our comprehensive standard deviation calculator offers two calculation modes for precise statistical analysis:

šŸ“Š Population Standard Deviation

Use when you have data for the entire population. The formula divides by N (total count) and uses the symbol Ļƒ (sigma). Perfect for complete datasets where you want to measure the spread of all values.

šŸ“ˆ Sample Standard Deviation

Use when your data represents a sample from a larger population. The formula divides by N-1 (degrees of freedom) and uses the symbol s. This provides an unbiased estimate of population standard deviation.

Simply enter your numbers separated by commas or spaces, and get instant results including mean, variance, and detailed statistical breakdowns. Our standard deviation tool handles any size dataset with precision.

Frequently Asked Questions

What's the difference between population and sample standard deviation?
Population standard deviation (Ļƒ) divides by N and is used when you have data for the entire population. Sample standard deviation (s) divides by N-1 and is used when your data represents a sample from a larger population.
How do I enter my data?
Enter numbers separated by commas, spaces, or new lines. For example: "1, 2, 3, 4, 5" or "1 2 3 4 5". The calculator automatically processes your input format.
What does standard deviation measure?
Standard deviation measures the spread or dispersion of data points from the mean. A low standard deviation indicates data points are close to the mean, while a high standard deviation indicates more spread out data.
How is variance related to standard deviation?
Variance is the square of standard deviation. Standard deviation is the square root of variance. Both measure data spread, but standard deviation is in the same units as your original data.