Standard Deviation Calculator
Calculate standard deviation, variance, mean, and data spread instantly. Use our free Standard Deviation Calculator for statistics, research, education, and data analysis.
Standard deviation measures the average statistical dispersion of data points around the arithmetic mean. It provides both Population Standard Deviation $(\sigma = \sqrt{\frac{\sum (x_i - \mu)^2}{N}})$ for complete census datasets and Sample Standard Deviation $(s = \sqrt{\frac{\sum (x_i - \bar{x})^2}{n - 1}})$ utilizing Bessel's correction $(n-1)$ to eliminate bias when inferring population parameters from subset samples.
Standard Deviation Calculator
Calculate standard deviation, variance, mean, range, and other statistical measures from a dataset.
Gaussian Normal Distribution & Empirical Rule (68–95–99.7)
68.27% (±1σ) | 95.45% (±2σ) | 99.73% (±3σ)For standard normal distributions $\mathcal{N}(\mu, \sigma^2)$, approximately 68.3% of observations lie within 1 standard deviation of the mean, 95.5% within 2 standard deviations, and 99.7% within 3 standard deviations (the 3-sigma process capability threshold).
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How the Standard Deviation Calculator Works
Follow these simple steps to get accurate results instantly.
Enter Data Values
Enter numbers separated by commas.
Calculate Mean
The calculator finds the average of all values.
Calculate Variance
Variance is calculated using deviations from the mean.
View Standard Deviation
See standard deviation, variance, mean, and count.
Standard Deviation Formula
σ = √( Σ(x − μ)² / N )
Standard deviation measures how spread out data values are from the mean. A low standard deviation indicates data points are close to the mean, while a high standard deviation indicates greater variability.
Example Calculation
Input: 10, 20, 30, 40, 50
Output: Mean = 30, Standard Deviation ≈ 14.14
Common Uses
- • Statistics
- • Research
- • Data Analysis
- • Education
- • Business Analytics
- • Data Science
- • Survey Analysis
- • Mathematics
- • Scientific Studies
- • Quality Control
Frequently Asked Questions
Verified answers to essential calculation and diagnostic questions.
Standard deviation measures how much data values differ from the average value.
A low standard deviation indicates that data points are clustered close to the mean.
A high standard deviation indicates that data values are spread out over a wider range.
Variance is the average of squared differences from the mean and is used to calculate standard deviation.
Standard deviation is used in statistics, finance, research, data science, engineering, and quality control.
Yes. Many statistical analyses use sample standard deviation when working with a subset of a population.
It saves time, reduces calculation errors, and helps analyze data variability quickly.
Population standard deviation divides by N (total population size), while sample standard deviation divides by n - 1 (Bessel's correction) to correct for bias when estimating population variability from a sample.
Written & maintained by Aditya Singh
Aditya Singh is a software engineer and the founder of DevCalc, based in Uttar Pradesh, India. He builds and maintains every calculator on this site, using standard, verified formulas — the same ones used by banks, institutions, and educators — with careful attention to accuracy. Read more about the author →