Standard Deviation Calculator
Compute the standard deviation, variance, mean, and sum of your data set instantly. Handles both entire group (population) and partial subset (sample) algorithms.
Data Entry
What kind of data is this?
Statistical Output
Standard Deviation (σ)
4.90
Empirical Rule (68% Check)
Data Distribution Plot
Step-by-Step Variance Table
| Point # | Value (x) | Distance (x - μ) | Squared (x - μ)² |
|---|---|---|---|
| 1 | 10.00 | -8.00 | 64.00 |
| 2 | 12.00 | -6.00 | 36.00 |
| 3 | 23.00 | 5.00 | 25.00 |
| 4 | 23.00 | 5.00 | 25.00 |
| 5 | 16.00 | -2.00 | 4.00 |
| 6 | 23.00 | 5.00 | 25.00 |
| 7 | 21.00 | 3.00 | 9.00 |
| 8 | 16.00 | -2.00 | 4.00 |
Complete Math Guide
Mastering the Standard Deviation Calculator
Welcome to the most precise and user-friendly Standard Deviation Calculator available online. When dealing with raw numbers, finding the average (mean) is only half the battle. If I tell you the average temperature of two cities is 70°F, you might think they have identical climates. However, if one city is always exactly 70°F, and the other swings between 40°F and 100°F, their statistical realities are vastly different.
Standard deviation is the mathematical tool that solves this problem. It is a strict measure of variation or dispersion within a set of data. This calculator instantly computes exactly how scattered your data points are from the center. It eliminates the tedious process of calculating individual squared differences manually, providing not just the final result, but a full variance table and a visual distribution plot.
Frequently Asked