Standard Deviation Calculator
Calculate standard deviation, variance, mean, and other descriptive statistics.
Enter Your Data
Calculation Type
Use when analyzing a sample from a larger population.
Data Distribution
0
s = √(Σ(xᵢ - μ)² / N-1)
Mean (μ)
0
Variance
0
CV
0%
Count
0
Median
0
Mode
None
Range
0
Min
0
Max
0
Standard deviation quantifies how far data points typically fall from the average. Low SD means values cluster near the mean; high SD means wider dispersion.
What standard deviation tells you
Mean gives the center of data; standard deviation gives the spread. In finance, SD of returns measures volatility. In manufacturing, SD tracks process consistency.
Variance is SD squared. SD restores units (e.g. dollars, kg) making interpretation easier than variance alone.
Population vs sample formulas
Choose population formulas when your dataset is complete. Use sample formulas with n−1 (Bessel’s correction) when inferring about a larger group.
Standard deviation is the square root of variance, restoring the same units as your original data.
Population SD
Sample SD
Variance
Interpreting results
Coefficient of variation (CV) helps compare spread when means differ—e.g. SD of 2 on mean 10 (CV 20%) vs SD of 5 on mean 100 (CV 5%).
For normally distributed data, about 68% of values fall within one SD of the mean, and ~95% within two SDs.
Last updated: August 6, 2026
Frequently Asked Questions
Explore More
Related Calculators
Correlation
Calculate Pearson correlation (r) and linear regression.
Mean, Median, Mode
Calculate central tendency, range, and distribution stats.
Percentile
Calculate percentiles, quartiles, and IQR.
Variance
Calculate variance and standard deviation for datasets.
ANOVA (One-Way)
Compare means of 3+ groups using F-test.
Bayes Theorem Calculator
Calculate conditional probability P(A|B) using priors.