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Calculate standard deviation, variance, and mean.
📊 Population stddev divides by N; sample stddev (Bessel's correction) divides by N−1. Both are shown above.
Standard deviation measures how spread out a set of numbers is from the average. A small standard deviation means values cluster tightly around the mean; a large one means they're widely scattered. This is one of the most useful statistics in data analysis.
If test scores have a mean of 75 with a standard deviation of 5, most scores fall between 70 and 80. With the same mean but a standard deviation of 15, scores spread from 60 to 90. Same average — very different picture.
For normally distributed data: ~68% of values fall within 1 standard deviation of the mean, ~95% within 2, and ~99.7% within 3. So if adult heights average 170 cm with SD 7, about 95% of people are between 156 and 184 cm.
This calculator uses population standard deviation (divides by N). If your data is a sample from a larger population, use sample standard deviation (divides by N−1) to get an unbiased estimate. Multiply our result by √(N/(N−1)) to convert.
The Standard Deviation Calculator lets you figure out standard deviation calculatorinstantly, without reaching for a spreadsheet or doing the math by hand. Whether you're planning a budget, checking a loan, or working through homework, the tool applies the correct formula behind the scenes and shows the result the moment you enter your numbers.
Unlike a static chart or table, this calculator adapts to your exact inputs. You can adjust any value and see the outcome update in real time, which makes it easy to compare scenarios — for example, "what if the rate were 1% lower?" or "what if I paid an extra $50 a month?"
Common uses: people reach for this tool when they need to find a standard deviation calculator with steps, population vs sample standard deviation, variance and mean calculator, or standard deviation of data set.
Browser-based tools like this one have a few real advantages over installed software or manual methods:
The Standard Deviation Calculator is based on the following formula:
σ = √[ Σ(xᵢ − x̄)² / n ]
Variables: σ = Population standard deviation xᵢ = Each data point x̄ = Mean of the data n = Number of data points
Population standard deviation. x̄ is the mean, n is the number of data points. Sample standard deviation uses n−1 in the denominator.
Worked example: Step 1: Data 2, 4, 4, 4, 5, 5, 7, 9: n = 8, x̄ = 40 / 8 = 5. Step 2: Squared deviations: 9 + 1 + 1 + 1 + 0 + 0 + 4 + 16 = 32. Step 3: Variance = 32 / 8 = 4. Step 4: σ = √4 = 2. Result: the population standard deviation is 2.
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