Free Online Standard Deviation Calculator
Get mean, variance, and standard deviation from any data set
Calculate mean, variance, and standard deviation from any data set.
8 numbers parsed
Mean
18
Pop. Std Dev (σ)
4.899
Sample Std Dev (s)
5.2372
Pop. Variance (σ²)
24
Sample Variance (s²)
27.4286
Count (n)
8
Sum
144
Min
10
Max
23
Range
13
Step-by-Step Calculation
Step 1: Find the mean
Mean = (10 + 12 + 23 + 23 + 16 + 23 + 21 + 16) / 8 = 18
Step 2: Find squared differences from the mean
(10 − 18)² = 64
(12 − 18)² = 36
(23 − 18)² = 25
(23 − 18)² = 25
(16 − 18)² = 4
(23 − 18)² = 25
(21 − 18)² = 9
(16 − 18)² = 4
Step 3: Find variance
Population variance (σ²) = 192 / 8 = 24
Sample variance (s²) = 192 / 7 = 27.4286
Step 4: Take the square root
Population std dev (σ) = √24 = 4.899
Sample std dev (s) = √27.4286 = 5.2372
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Why use Standard Deviation Calculator
- Reports both population (sigma) and sample (s) standard deviation side by side.
- Flexible parser handles commas, spaces, tabs, and newlines -- paste from Excel, Google Sheets, or a plain text file.
- Full descriptive stats suite (mean, variance, min, max, range, sum, count) in one pass.
- Step-by-step breakdown shows the calculation at each stage, useful for verifying homework or understanding a discrepancy.
- Count confirmation catches silent copy-paste errors before you rely on the result.
- No login, no data retention -- useful for sensitive research data you would rather not upload to a cloud stats tool.
How it works
The calculator parses input by splitting on commas, whitespace, or newlines and converting each token to a number, discarding non-numeric entries. Mean is sum divided by count (N). Variance subtracts the mean from each value, squares the difference, sums those squares, and divides by N (population) or N-1 (sample, Bessel's correction). Standard deviation is the square root of variance. Min, max, range, and sum are computed as bonus descriptive statistics in the same pass.
About this tool
Paste a column of numbers -- from a spreadsheet, a comma-separated list, or one value per line -- and get population and sample standard deviation, variance, mean, sum, min, max, range, and data point count. The parser is flexible: commas, spaces, tabs, and line breaks all work, and a count confirms nothing was dropped. Both population SD (dividing by N) and sample SD (dividing by N-1, Bessel's correction) are reported because the distinction matters. If your data is a subset of a larger group -- which is almost always the case in academic and real-world analysis -- the sample version is the one to cite. A step-by-step section walks through the math: find the mean, subtract it from each value, square the differences, sum them, divide by N or N-1, take the square root. Useful when you need to verify a manual calculation or show your work.
How to use Standard Deviation Calculator
- Paste or type your data. Enter numbers separated by commas, spaces, tabs, or line breaks. Paste a spreadsheet column directly.
- Confirm the count. Check the reported data point count matches what you expect -- catches copy-paste errors.
- Read the statistics. Population SD, sample SD, mean, variance, min, max, range, sum, and count all appear at once.
Use cases
- QC engineer pasting batch measurements to check whether product dimensions fall within acceptable variability.
- Statistics student verifying a hand-calculated standard deviation before submitting the problem set.
- Teacher grading exams who needs the class average, score spread, and a quick sense of the distribution shape.
Frequently Asked Questions
Standard deviation measures how spread out numbers are from the mean (average). A low standard deviation means values cluster near the mean; a high one means they are spread out. It is the square root of variance.
Population standard deviation (σ) divides by N (total count). Sample standard deviation (s) divides by N−1 to correct for the bias of estimating a population from a sample. Use sample SD when your data is a subset of a larger population.
1) Find the mean. 2) Subtract the mean from each value and square the result. 3) Find the average of those squared differences (variance). 4) Take the square root. That's your standard deviation.
It depends entirely on context. A standard deviation of 5 is tiny for stock prices but huge for exam scores out of 10. Compare it to the mean -a coefficient of variation (SD ÷ mean × 100) below 15% is generally considered low variability.
Variance is the average of the squared differences from the mean. It is standard deviation squared. While variance is useful in many statistical formulas, standard deviation is more intuitive because it is in the same units as the data.
Enter numbers separated by commas, spaces, line breaks, or any combination. The calculator parses your input and shows how many values it detected so you can verify.
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