Standard Deviation Calculator
Calculate mean, variance, and standard deviation for a list of numbers.
Inputs
Result
Enter values on the left and select Calculate to see the result here.
What the Standard Deviation Calculator does
- Calculates the mean, variance, and standard deviation for the numbers you enter.
- Supports both sample standard deviation and population standard deviation; the current default mode is Sample.
- Helps with educational and statistical checks, but it is not professional statistical, scientific, medical, financial, or legal advice.
How to use the Standard Deviation Calculator
- Enter numeric values separated by commas or spaces, such as 2, 4, 4, 4, 5, 5, 7, 9.
- Choose Sample when your data is a subset used to estimate a larger population, or Population when the list is the entire group you want to describe.
- Click Calculate and review the data for entry errors, outliers, and whether standard deviation is appropriate for your context.
Formula / methodology used
- Standard deviation describes typical spread: a smaller value means numbers are closer to the mean, while a larger value means they are more spread out.
- Mean = sum of values ÷ number of values.
- Population variance = sum of squared deviations from the mean ÷ n; population standard deviation = square root of that variance.
- Sample variance = sum of squared deviations from the mean ÷ (n−1); sample standard deviation = square root of that variance. In this implementation, a one-value sample uses a denominator of 1 to avoid division by zero, so the displayed spread is 0.
- Displayed mean, variance, and standard deviation are rounded to 6 decimal places.
Example calculation
Numbers: 2, 4, 4, 4, 5, 5, 7, 9 in population mode.
- Mean = (2+4+4+4+5+5+7+9) ÷ 8 = 40 ÷ 8 = 5
- Squared deviations from 5 are 9, 1, 1, 1, 0, 0, 4, and 16
- Sum of squared deviations = 32
- Population variance = 32 ÷ 8 = 4
- Population standard deviation = sqrt(4) = 2
Result: In population mode, the calculator would show mean 5, variance 4, and standard deviation 2. In sample mode for the same data, variance would be 32 ÷ 7 = 4.571429 and standard deviation about 2.13809.
Common mistakes and limitations
- The result depends on the numbers entered; invalid non-numeric entries are ignored after splitting by spaces or commas.
- Small samples, one-value samples, outliers, skewed data, non-normal distributions, and measurement errors can make interpretation difficult.
- Standard deviation is only one summary statistic and may be inappropriate without context, charts, domain knowledge, or formal statistical analysis.
Important note
This standard deviation calculator is an educational/statistical helper based on your entered numbers. It is not professional statistical, scientific, medical, financial, legal, or research advice.
Standard Deviation Calculator FAQs
Does this use sample or population standard deviation?
It supports both. Select Sample to divide squared deviations by n−1, or Population to divide by n. The default selection is Sample.
What does standard deviation mean in plain language?
It is a measure of how spread out the numbers are around the mean. It does not by itself prove that data is normal, fair, accurate, or meaningful.
Can outliers or small samples affect the result?
Yes. Small datasets, outliers, skewed or non-normal distributions, and data-entry errors can strongly affect standard deviation and how it should be interpreted.