Standard Deviation Calculator
Use this professional standard deviation calculator to quickly find the mean, variance, sample standard deviation, population standard deviation, sum, and total count from any data set.
Enter Your Data Set
You can separate values using commas, spaces, or new lines. Only numeric values will be calculated.
Results
Standard deviation shows how spread out numbers are from the average value. A small standard deviation means most values are close to the mean, while a large standard deviation means values are more spread out.
This calculator is useful for students, researchers, finance users, business reports, quality checks, surveys, and any situation where you need to understand data variation.
- Enter your numbers separated by commas, spaces, or new lines.
- Choose sample or population standard deviation.
- The tool calculates the mean of your data set.
- It finds how far each number is from the mean.
- It returns standard deviation, variance, count, and sum instantly.
Use sample standard deviation when your data is only a part of a bigger group, such as a survey of 50 customers from thousands.
Use population standard deviation when your data includes every value in the complete group, such as marks of every student in one small class.
- Fast and accurate statistical calculations
- Supports comma, space, and line-separated values
- Calculates sample and population deviation
- Shows mean, variance, count, and sum together
- Works directly in your browser without page reload
Population standard deviation divides the total squared deviation by the full population size:
Sample standard deviation uses Bessel's correction and divides by one less than the sample size:
Here, xᵢ is each value, μ is the population mean, x̄ is the sample mean, and N or n is the number of values.
For the data set 2, 4, 4, 4, 5, 5, 7, 9:
- Count: 8
- Mean: 5
- Sum of squared deviations: 32
- Population variance: 32 ÷ 8 = 4
- Population standard deviation: √4 = 2
- Sample standard deviation: √(32 ÷ 7) ≈ 2.13809
Standard deviation uses the same unit as the original values. Its meaning depends on the subject, measurement scale, and comparison group, so there is no universal number that is always “high” or “low.”
| Result | What it usually means | What to check |
|---|---|---|
| 0 | Every value in the data set is identical. | Confirm that repeated values are expected and not a data-entry issue. |
| Small relative to the mean | Values are clustered fairly close to the average. | Compare with a similar data set measured in the same unit. |
| Large relative to the mean | Values are more widely dispersed. | Look for outliers, mixed groups, or genuine variation. |
Frequently Asked Questions
What does standard deviation tell you?
Standard deviation shows how far values typically lie from the mean. A lower value indicates that the data is more tightly grouped, while a higher value indicates greater spread.
Should I use sample or population standard deviation?
Use sample standard deviation when the values are a sample from a larger group. Use population standard deviation when the values represent every member of the complete population.
Can I paste numbers from Excel?
Yes. You can paste numbers from Excel, Google Sheets, or another list. Values may be separated by commas, spaces, tabs, semicolons, or new lines.
What is variance?
Variance is the average squared distance from the mean. Standard deviation is the square root of variance, so it is expressed in the same unit as the original data.
Is this calculator useful for statistics homework?
Yes. It can check standard deviation, variance, mean, count, and sum for statistics homework, data analysis, research, quality control, and business reports.