Free Standard Deviation Calculator - Measure Data Spread
Calculate standard deviation, variance, and statistical measures. Best free SD calculator 2025 - population and sample calculations.
Quick Answer
Standard deviation measures how spread out numbers are from the mean. Calculate: 1) Find mean, 2) Subtract mean from each value and square, 3) Average the squared differences (variance), 4) Take square root. Low SD means data is clustered near mean; high SD means data is spread out. Calculate at practicalwebtools.com.
Key Facts about Standard Deviation Calculator:
- Standard deviation = √variance
- Population SD: σ = √[Σ(x-μ)²/N]
- Sample SD: s = √[Σ(x-x̄)²/(n-1)]
- About 68% of data falls within 1 SD of mean (normal distribution)
- 95% within 2 SD, 99.7% within 3 SD
- SD of 0 means all values are identical
- Variance is SD squared
Why Use Our Standard Deviation Calculator?
Comprehensive statistics:
Standard Deviation
Population and sample SD.
Variance
Squared deviation measure.
Mean
Average of your data.
Range
Min, max, and spread.
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How to Standard Deviation Calculator in 3 Easy Steps
Calculate standard deviation:
Enter Data
Type or paste your numbers.
Choose Type
Population or sample SD.
Get Results
View SD, variance, and more.
Understand Data Spread
Measure variability in data
Both population and sample formulas
Complete statistical summary
Essential for statistics
Common Use Cases for Standard Deviation Calculator
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Frequently Asked Questions
Everything you need to know about our standard deviation calculator
What is standard deviation?
Measures how spread out data is from the average.
Standard deviation measures how spread out numbers are from their average (mean). Higher SD means more spread; lower SD means more clustered around the mean.
Population vs sample standard deviation?
Population divides by N; sample divides by n-1 for unbiased estimate.
Population SD (σ) divides by N (total count). Sample SD (s) divides by n-1 (Bessel correction) for unbiased estimation when working with a sample of a larger population.
What is variance?
Variance = SD². Average squared distance from mean.
Variance is standard deviation squared. It measures the average squared distance from the mean. SD is the square root of variance.
What does SD tell us about data?
68% within 1 SD, 95% within 2 SD. Low SD = consistent.
For normal distributions: 68% of data within 1 SD, 95% within 2 SD, 99.7% within 3 SD. Low SD = consistent data; high SD = variable data.
Still have questions? Try the tool yourself!
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