Standard Deviation Calculator
Find how spread out a set of numbers is: the mean, the variance and the standard deviation, for a sample or a whole population, with every squared deviation shown so you can check the working.
Runs in your browser. Your data is not uploaded.How our tools work
Separate numbers with commas, spaces or new lines. Use a point for decimals, such as 2.5.
How do I calculate standard deviation?
Find the mean, subtract it from each value, square the differences and add them up. Divide by the number of values for a population, or by one less for a sample, and take the square root. For 2, 4, 4, 4, 5, 5, 7 and 9 the population standard deviation is 2 and the sample one is 2.14.
- Enter or paste your numbers, separated by commas, spaces or new lines.
- Choose Sample if the numbers are a sample from a larger group, or Population if they are the whole group.
- Read the standard deviation, variance and mean, and open the step-by-step table to check each squared deviation.
Formulas & Methods
Mean
Example: 40 ÷ 8 = 5
Population standard deviation
Example: √(32 ÷ 8) = √4 = 2
Sample standard deviation
Example: √(32 ÷ 7) = √4.571 = 2.138
Variance
Example: population 4, sample 4.571
Key features
Sample or population, stated
You choose which formula applies, and the other is shown too, so nothing is assumed silently.
Step-by-step table
Each value with its deviation from the mean and the squared deviation, as you would write it out by hand.
Common uses
- Check a statistics homework answer step by step
- Measure how consistent test scores, delivery times or measurements are
Sample or population?
Use population when your numbers are every member of the group you care about: all the students in one class, every order last month. Use sample when they are a selection used to describe something bigger: 30 customers surveyed out of thousands. Dividing a sample by N − 1 (Bessel’s correction) corrects for the fact that a sample’s values sit closer to their own mean than to the true mean of the whole group.
Spreadsheets follow the same split: STDEV.S or STDEV for a sample, STDEV.P for a population.
Frequently Asked Questions
What does the standard deviation tell me?
How far values typically are from the mean, in the same units as the data. Test scores with a mean of 70 and a standard deviation of 5 are bunched together; with 20 they are widely spread.
Why is the sample standard deviation larger?
Because it divides by N − 1 instead of N, a smaller number. The difference shrinks as the sample grows: with 100 values it is about half a percent.
Why is there no sample result for a single number?
One value can’t show any spread, and dividing by N − 1 = 0 is impossible, so a sample needs at least two values. The population result for one value is 0.
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