Online Standard Deviation Calculator
Standard Deviation Calculator finds the sample and population standard deviation, variance, mean, count, and sum of squares from a list of numbers.
Comma-separated numbers
| Sample | Population | |
|---|---|---|
| Standard Deviation | σ = 5.3385 | s = 4.9937 |
| Variance | σ² = 28.5 | s² = 24.9375 |
| Count | n = 8 | n = 8 |
| Mean | μ = 18.25 | x̄ = 18.25 |
| Sum of squares | SS = 199.5 | SS = 199.5 |
What Is This Tool?
The Standard Deviation Calculator measures how spread out a set of numbers is. Enter your values separated by commas or spaces, and it returns both the sample and population standard deviation, along with the variance, count, mean, and sum of squares. The sample figures divide by n−1 and the population figures divide by n, so you can pick whichever matches your data. The result can be downloaded as a PDF.
How to Use This Tool?
- Enter your numbers separated by commas or spaces.
- Make sure you provide at least two values.
- Click Calculate to see the full set of statistics.
- Download a PDF of the result if you'd like.
Key Features
- Calculates both sample and population standard deviation.
- Also reports variance, count, mean, and sum of squares.
- Accepts numbers separated by commas or spaces.
- Shows results side by side for easy comparison.
- Offers a one-click PDF download of the result.
Examples
- The set 9, 12, 23, 22, 16, 21, 20, 23 has a mean of 18.25.
- Its sample standard deviation is about 5.3385.
- Its population standard deviation is about 4.9937.
- The sum of squares for that set is 199.5.
Common Use Cases
- Measuring the spread of test scores or measurements.
- Checking variability in experimental or survey data.
- Comparing the consistency of two data sets.
- Completing statistics homework or coursework.
- Summarizing data before further analysis.
Tips & Best Practices
- Use the sample figures when your data is a subset of a larger group.
- Use the population figures when your data covers the whole group.
- Double-check that every value is a number before calculating.
- Separate values consistently with commas or spaces.
- Keep the mean and sum of squares for verifying the result by hand.
Limitations
- Results are only as accurate as the numbers you enter.
- Non-numeric entries are ignored rather than flagged individually.
- At least two values are required to compute a standard deviation.
- Nothing is saved between sessions — only the current result can be exported as a PDF.
Frequently Asked Questions
- What's the difference between sample and population standard deviation?
- The sample version divides by n−1 and the population version divides by n; use the sample one when your data is a subset of a larger group.
- How do I enter my data?
- Type your numbers separated by commas or spaces — both work.
- What is the sum of squares?
- It's the total of each value's squared difference from the mean, the basis for variance.
- Why do I need at least two numbers?
- Standard deviation measures spread, which isn't defined for a single value.
Key Terminology
- Standard deviation
- A measure of how spread out the values in a data set are.
- Variance
- The average of the squared differences from the mean; the square of the standard deviation.
- Mean
- The arithmetic average of all the values.
- Sum of squares
- The total of each value's squared difference from the mean.
- Sample vs. population
- Sample statistics divide by n−1 for a subset; population statistics divide by n for the whole group.