Standard Deviation Calculator
Calculate the standard deviation and variance of a set of numbers.
Tip: High standard deviation = spread-out data; low = clustered around the mean.
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About this digital tool
The standard deviation calculator shows how far the values of a list spread from the mean. Enter the numbers separated by commas, spaces or new lines and get the standard deviation, variance, mean and range. A small deviation means the values are clustered close to the mean, a large one that they are spread out.
The steps are: find the mean, calculate the squares of each value's distance from the mean, add them up and divide by the number of values (this is the variance), then take the square root. For 2, 4, 4, 4, 5, 5, 7, 9 the mean is 5, the sum of squared distances is 32, the variance 32 ÷ 8 = 4 and the standard deviation 2. This calculator divides by N, so it gives the population deviation.
How to use
- Enter the values (separated by commas or spaces).
- Choose population or sample.
- See the standard deviation, variance and other statistics.
Frequently asked questions
What is the difference between population and sample?
The population deviation (σ) divides by N; the sample one (s) by N−1. Use the sample when the data is part of a larger group.
How is standard deviation calculated step by step?
Find the mean, subtract the mean from each value, square the results, add them up, divide by N and take the square root. For 2, 4, 4, 4, 5, 5, 7, 9 it comes to 2.
What is variance?
Variance is the square of the standard deviation, that is the average of the squared distances from the mean. If the standard deviation is 2, the variance is 4.
How do I get the sample standard deviation with this calculator?
The calculator divides by N. For a sample, multiply the result by √(N ÷ (N − 1)). E.g. for 2, 4, 4, 4, 5, 5, 7, 9 it comes to 2 × √(8/7) ≈ 2.14.