Standard Deviation Calculator
Paste your numbers and get the standard deviation, variance, mean, median, range and more — with a toggle for sample (n−1) or population (n) calculations.
Enter Your Data
Standard Deviation
6.149
Mean 20.143 · Variance 37.81 · 7 values
Count
7
Mean (average)
20.143
Standard Deviation
6.149
Variance
37.81
Median
20
Sum
141
Min / Max
12 / 30
Range
18
How It Works
Standard deviation measures how spread out a set of numbers is around their average. A small standard deviation means the values cluster tightly near the mean; a large one means they are widely scattered. The calculation first finds the mean, then the average of the squared differences from that mean (the variance), and finally the square root of the variance (the standard deviation, back in the original units). A key choice is the divisor: use the sample method (dividing by n − 1) when your data is a sample drawn from a larger population — this corrects a bias and is the usual choice in statistics — and the population method (dividing by n) when you have the entire set. This calculator accepts numbers separated by commas, spaces or new lines and reports the standard deviation, variance, mean, median, sum, minimum, maximum and range together.
Formula
Variance = Σ(x − mean)² ÷ N, where N = n for population or n−1 for a sample. Standard deviation = √variance.
Frequently Asked Questions
What is the difference between sample and population standard deviation?
The population version divides by n; the sample version divides by n − 1 (Bessel’s correction) to give an unbiased estimate when your data is only a sample of a larger group. Use the sample method unless you have every data point.
How is standard deviation calculated?
Find the mean, then the average of the squared differences from the mean (the variance), then take the square root. The calculator does all of this and shows the intermediate values.
What does a high standard deviation mean?
That the data points are spread far from the average — there is high variability. A low standard deviation means the values are close to the mean and more consistent.
What is variance versus standard deviation?
Variance is the average squared deviation from the mean; standard deviation is its square root. Standard deviation is usually preferred because it is in the same units as the data.
How do I enter my data?
Type or paste numbers separated by commas, spaces or new lines — for example “12, 15, 17, 20”. The calculator ignores blanks and non-numbers and updates instantly.