Standard Deviation Calculator
Standard deviation measures data spread from the mean (average). Formula: σ = √[Σ(x - μ)² / N]. Steps: 1) Find mean μ, 2) Subtract mean from each value and square, 3) Average those squares (variance), 4) Take square root. For data [2,4,4,4,5,5,7,9]: mean=5, variance=4, SD=2. Low SD = data clustered near mean, high SD = data spread out. Sample SD (n-1 denominator) for samples, population SD (N denominator) for entire population. Use in statistics, quality control, finance (volatility).
Calculate standard deviation, variance, mean, median, and other statistics. Supports both population and sample calculations.
Enter Numbers
Separate numbers with commas, spaces, or new lines
Data Type
Use sample when your data is a subset of a larger population
Standard Deviation (σ)
5.237229
Mean (Average)
18
Variance (σ²)
27.428571
Count
8
Sum
144
Min
10
Max
23
Median
18.5
Range
13
Coefficient of Variation
29.095719%
Understanding Standard Deviation
- Standard deviation measures how spread out values are from the mean
- Low SD = values are close together; High SD = values are spread apart
- ~68% of values fall within 1 SD of the mean in normal distributions
- ~95% of values fall within 2 SDs of the mean
- Sample SD divides by (n-1) to correct for bias when estimating population SD
How to Use
- Enter your value in the input field
- Click the Calculate/Convert button
- Copy the result to your clipboard
Frequently Asked Questions
- What is standard deviation?
- Standard deviation (σ or SD) measures how spread out data is from the mean. Low SD = data clustered near average. High SD = data spread widely. Calculated as square root of variance. About 68% of data falls within 1 SD of mean in normal distributions.
- What is the difference between population and sample standard deviation?
- Population SD (σ) divides by n (total count). Sample SD (s) divides by n-1 to correct for bias when estimating from a subset. Use population when you have ALL data. Use sample when data represents a larger group.
- How do I interpret standard deviation?
- In normal distributions: ~68% within 1 SD, ~95% within 2 SDs, ~99.7% within 3 SDs of mean. Example: test scores with mean 75, SD 10 means most scores between 65-85. Low SD = consistent, high SD = variable.
- What is variance?
- Variance is the average of squared differences from the mean. Standard deviation = √variance. Variance is useful mathematically but in squared units (dollars², cm²). SD is in original units, more interpretable.
- How is standard deviation used in finance?
- SD measures investment volatility/risk. Higher SD = more price variation = riskier. S&P 500 historical SD is ~15-20%. Low-risk bonds: 3-5% SD. Individual stocks can exceed 30%. Investors balance expected return against SD.