Standard Deviation Calculator

Enter your data to get a complete descriptive statistics summary including standard deviation, variance, mean, median, mode, quartiles, and more.

Enter Data

Enter numbers separated by commas, spaces, or new lines. Up to 10,000 values supported.

Decimal places

Data type

Sample Population

Key Results

Sample Std Dev (s)

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Population Std Dev (σ)

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Mean (x̄)

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Median

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Count (n)

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Full Statistics Summary

Statistic	Value	Statistic	Value

Distribution Histogram

Sorted Data & Frequency Table

Sorted data (ascending)

Frequency table

Value	Frequency	Rel. Freq.	Cum. Freq.

Standard Deviation Explained

Standard deviation measures the amount of variation or dispersion in a dataset. A low standard deviation indicates values are clustered near the mean; a high standard deviation indicates values are spread widely.

Sample vs Population Standard Deviation

Population (σ): Use when your data represents the entire population. Divides by n.
Formula: σ = √(Σ(xᵢ − μ)² / n)

Sample (s): Use when your data is a sample from a larger population. Divides by n−1 (Bessel's correction to account for sampling bias).
Formula: s = √(Σ(xᵢ − x̄)² / (n−1))

Empirical Rule (68-95-99.7)

For normally distributed data: approximately 68% of values fall within ±1σ of the mean; 95% within ±2σ; 99.7% within ±3σ. This is widely used in quality control, finance, and science.

Coefficient of Variation (CV)

CV = (s / x̄) × 100%. It expresses standard deviation as a percentage of the mean, allowing comparison of variability between datasets with different units or scales.