Free Online Standard Deviation Calculator

A standard deviation calculator measures the spread or dispersion of data points around the mean, quantifying variability in datasets. Low standard deviation indicates data clustered tightly around the average; high standard deviation shows wide scattering. Essential for statistics, quality control, finance, scientific research, manufacturing, and data analysis across every industry.

Enter your dataset and instantly receive population standard deviation (σ), sample standard deviation (s), variance, mean, and complete statistical summary. Handles both small samples and massive datasets with high precision, showing step-by-step calculations and 68-95-99.7% confidence intervals for normal distributions—perfect for students, analysts, researchers, and business professionals.

What is Standard Deviation?

Standard deviation quantifies average distance of data points from the mean. In [3, 4, 5], mean=4, deviations=(1,0,1), average deviation=0.67, but standard deviation

Population σ uses N (all data). Sample s uses n-1 (unbiased estimator). [10,12,14] gives σ=1.63 (N=3), s=2 (n-1=2). Sample correction prevents underestimation from small datasets.

68% data falls within ±1σ, 95% within ±2σ, 99.7% within ±3σ (normal distribution). Quality control rejects beyond 3σ. Finance uses σ=risk/volatility. Manufacturing targets low σ=consistent production.

Standard Deviation Formulas

Step-by-Step Calculation Process

Example: [12, 15, 11, 14, 13]

How to Use the Calculator

1. 1.Enter data separated by commas, spaces, or new lines. Handles decimals and negatives.
2. 2.Choose Population (σ) or Sample (s). Sample for survey data, population for complete datasets.
3. 3.Click Calculate. Get σ/s, variance, mean, range, quartiles, confidence intervals instantly.
4. 4.Copy results, download CSV, or visualize distribution with histogram.

Real-World Applications by Industry

Manufacturing & Quality Control

Finance & Investing

Scientific Research

• Laser wavelength: [632.8, 632.9, 632.7, 632.85]nm → σ=0.08nm ✓ Precise
• Reaction time: [2.1, 2.4, 1.9, 2.3, 2.0]s → σ=0.19s (normal human variation)
• DNA sequence error rate: σ=0.02% (quality control)

Interpreting Results

68-95-99.7 Rule (Empirical Rule)

Frequently Asked Questions

Population vs Sample?

Population (σ): Complete dataset (factory production run). Sample (s): Subset (quality check). Use s-1 denominator for unbiased small-sample estimation.

High standard deviation bad?

Depends on context. Manufacturing: bad (inconsistent). Finance: expected (market volatility). Biology: normal (natural variation).

Negative numbers OK?

Yes. Temperature [-5, 0, 3], profit/loss [-100, 50, 200], elevation differences all work perfectly.

Very large datasets?

Handles 10,000+ values instantly. Optimized algorithms prevent browser slowdown.

Export results?

Copy table, CSV download, JSON for developers. Full statistical report.

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This standard deviation calculator provides precise statistical analysis suitable for commercial quality control, financial risk assessment, manufacturing process monitoring, and business analytics. Verify mission-critical decisions with domain experts and validated methodologies.