Standard Deviation Calculator
Standard deviation measures how far the numbers spread from their mean — the dispersion of the data. Enter your values and pick population or sample to get the standard deviation, variance and mean.
Your numbers
Result
- Variance
- 4
- Mean
- 5
- Count
- 8
| Step | Value |
|---|---|
| Count | 8 |
| Mean | 5 |
| Variance (÷ n) | 4 |
| Standard deviation | 2 |
How it is calculated
First the mean. Then, for each value, the squared difference from the mean; add those up and divide by n (population) or n−1 (sample) to get the variance. The standard deviation is the square root of the variance. For 2, 4, 4, 4, 5, 5, 7, 9 (population): mean 5, variance 4, standard deviation 2.
Population or sample?
Use population (÷ n) when your data is the entire group. Use sample (÷ n−1) when it is a sample drawn from a larger group — dividing by n−1 (Bessel's correction) offsets the tendency of a sample to underestimate the true spread.
What the number tells you
A low standard deviation means values cluster near the mean; a high one means they are spread out. In a normal distribution, about 68% of values fall within one standard deviation of the mean and 95% within two — the basis of many statistical tests and confidence intervals.
Frequently asked questions
Sources
Embed this calculator
Copy the code and paste it into your site or blog. Credit with a link back to Contania is included, and the height adjusts itself.
<iframe src="https://contania.app/embed/math/standard-deviation" title="Standard Deviation Calculator (population & sample)" width="100%" height="720" loading="lazy" style="border:1px solid #e5e0d8;border-radius:12px;max-width:640px"></iframe>
<script>window.addEventListener("message",function(e){if(e.data&&e.data.type==="contania:embed-height"){var f=document.querySelector('iframe[src="https://contania.app/embed/math/standard-deviation"]');if(f){f.style.height=e.data.height+"px"}}});</script>Related calculators
Average
Calculate the mean, median, mode and range of a list of numbers, plus the sum and count. Enter your values separated by commas.
CalculateMathPercentage
Work out percentages three ways: what is X% of a number, what percent one number is of another, and finding the whole from a part and its percentage.
CalculateMathRatio
Simplify a ratio to its lowest terms, or solve a proportion to find a missing value. Enter two numbers to reduce A:B, or add a third to solve A:B = C:?.
CalculateMathTriangle
Enter the three sides of a triangle to get its perimeter, area (Heron’s formula) and type — by sides (equilateral, isosceles, scalene) and by angles (right, acute, obtuse).
CalculateMathVolume
Calculate the volume of a cube, box, sphere, cylinder, cone or pyramid. Pick the solid and enter its measurements to get the volume and the formula used.
CalculateMathArea
Calculate the area of a rectangle, square, triangle, circle or trapezoid. Pick the shape and enter its measurements to get the area and the formula used.
Calculate