Standard Deviation Calculator
Complete descriptive statistics.
Standard Deviation Calculator
Compute variance, standard deviation, and key statistics for any dataset.
Sample Std Deviation
Most commonly used
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What This Calculator Does
The Standard Deviation Calculator computes a full set of descriptive statistics from any list of numbers: mean, median, sample and population standard deviation, variance, min, max, and range.
How It Works
Enter numbers separated by commas, spaces, or newlines. The calculator parses them, computes the mean, then calculates deviation from the mean for each value. Sample deviation uses n-1 (Bessel correction); population uses n.
Example
For 4, 8, 6, 5, 3: mean = 5.2, sample std dev = 1.92, population std dev = 1.72.
Formula
Mean = Sum / Counts = sqrt(Sum((x - mean)^2) / (n-1))Reading the Results
Sample Std Dev
Standard deviation using n-1, appropriate for a sample of a larger population.
Population Std Dev
Standard deviation using n, appropriate when the data is the entire population.
Frequently Asked Questions
What is the difference between sample and population?
Sample standard deviation uses n-1 (Bessel correction) to estimate the true population parameter. Use it when your data is a subset. Population uses n and is exact for the full dataset.
What does standard deviation tell me?
It measures how spread out numbers are from the mean. A low std dev means values cluster near the mean; a high std dev means they are widely spread.
What input formats work?
Numbers separated by commas, spaces, or newlines. Mix formats in the same input: "1, 2 3 4" works fine.