Standard Deviation Calculator

How to use this calculator

Paste your numbers separated by commas or spaces and press Calculate. The tool reports both the sample and the population standard deviation, plus the variance, mean and count. Use the sample figure when your numbers are a sample drawn from a larger group, and the population figure when they represent the entire group. Decimals and negatives are accepted, so it suits test scores, lab measurements, financial returns and survey data alike.

The formula explained

Standard deviation is the square root of the average squared distance from the mean:

sample sd = √(Σ(x − mean)² ÷ (n − 1)) · population sd = √(Σ(x − mean)² ÷ n)

First you find the mean. Then for each value you measure how far it is from the mean, square that distance so positives and negatives do not cancel, and add them up. Dividing by the count (population) or the count minus one (sample) gives the variance, and the square root brings the answer back into the original units. The "minus one" for samples corrects a slight bias when estimating the spread of a larger group from a smaller sample.

A worked example

For 4, 8, 15, 16, 23, 42: the mean is 18. The squared distances from 18 add up to 910. The sample variance is 910 ÷ 5 = 182, so the sample standard deviation is √182 ≈ 13.49. The population version divides by 6 instead, giving √151.7 ≈ 12.32. The tool shows both.

Frequently asked questions

How do you calculate standard deviation?

Find the mean, square each value's distance from it, average those squares, then take the square root.

Sample vs population — which do I use?

Sample (÷ n−1) for a sample of data; population (÷ n) for a complete dataset.

What does it tell you?

How spread out the numbers are around the mean — small means tightly clustered, large means widely scattered.