Standard deviation solver
Separate values with commas, spaces, or new lines. Any mix works.
Use sample standard deviation when your data is a sample of a larger group. Use population standard deviation when you have every value.
Show the step-by-step calculation
Standard Deviation Solver
Paste a list of numbers and get sample and population standard deviation instantly, free, right in your browser.
Standard deviation measures how spread out a set of numbers is around its mean. A small standard deviation means the values cluster tightly together. A large one means they are scattered widely. It is one of the most used statistics in science, finance, quality control, and schoolwork, and this page computes it for you with no formulas to memorize.
Standard Deviation Solver reports both versions of the statistic. Sample standard deviation divides by n - 1 and is the correct choice when your numbers are a sample drawn from a larger group. Population standard deviation divides by n and applies when your list already contains every value you care about. Alongside both standard deviations you get sample and population variance, the sum of squared deviations, mean, median, minimum, maximum, and range, plus a step-by-step solution built from your actual data. Need just the variance? Try the variance calculator. Hunting for averages and the most frequent value? Use themean median mode calculator.
Everything runs on your device with plain JavaScript. Nothing you type is sent anywhere, there is no account, and the page works even on a slow connection.
Frequently asked questions
What is the difference between sample and population standard deviation?
Population standard deviation divides by n and is correct when your list contains every value in the group you care about. Sample standard deviation divides by n - 1 and is the right choice when your data is a sample taken from a larger group, because it corrects for the tendency of samples to underestimate the true spread.
Why does sample standard deviation divide by n - 1 instead of n?
This is called Bessel's correction. A sample's deviations are measured around the sample mean, which is fitted to that sample, so the raw average of squared deviations comes out slightly too small. Dividing by n - 1 instead of n inflates the result just enough to make the sample variance an unbiased estimate of the population variance.
What is the difference between variance and standard deviation?
Variance is the average of the squared deviations from the mean, so it is measured in squared units. Standard deviation is the square root of the variance, which brings the number back into the original units of your data and makes it much easier to interpret and compare.
Can I use negative numbers or decimals?
Yes. The solver accepts negative numbers, zero, and decimals in any mix. Every deviation from the mean is squared during the calculation, so variance and standard deviation are never negative no matter what values you enter.
What units does standard deviation have?
Standard deviation is measured in the same units as your data. If your numbers are heights in centimeters, the standard deviation is in centimeters. Variance is in squared units, such as centimeters squared, which is one reason standard deviation is usually the number people report.
When is the median more useful than the mean?
When your data is skewed or contains outliers, the mean gets pulled toward the extreme values and can stop representing a typical data point. Incomes and house prices are classic examples. In those cases the median, the middle value, gives a more honest picture of what is typical.
How many numbers do I need?
A single number already gives you count, sum, mean, median, minimum, maximum, and range. Sample standard deviation and sample variance need at least 2 values because dividing by n - 1 with one value would mean dividing by zero. Larger data sets give more reliable estimates of spread.
Does the order of the numbers matter?
No. Every statistic on this page is order independent. Shuffling your values changes nothing: the mean, median, variance, and standard deviation all come out identical, because they only depend on which values are present, not on their sequence.