General
Standard Deviation Calculator
Calculate population and sample standard deviation, variance, mean, and range with step-by-step formula breakdown.
Enter numbers and click Calculate
How is this calculated?
1. Mean (μ) = Σx / N
2. Squared differences = (x₁ - μ)² + (x₂ - μ)² + ...
3. Population Variance (σ²) = Σ(x - μ)² / N
4. Sample Variance (s²) = Σ(x - μ)² / (N - 1)
5. SD = √VarianceFAQ
Frequently asked questions
What is standard deviation?
Standard deviation measures how spread out numbers are from the mean. A low SD means data points cluster near the average; a high SD means they are spread over a wider range.
What is the difference between population and sample SD?
Population SD divides by N (total count). Sample SD divides by N-1 (Bessel correction) to account for estimating from a subset. Use sample SD when working with a subset of a larger population.
What is variance?
Variance is the square of standard deviation. It measures the average squared distance from the mean. SD is preferred for interpretation because it is in the same units as the data.
What does a high standard deviation mean?
A high SD indicates data is widely spread from the mean. In investing, high SD means high volatility. In manufacturing, it means inconsistent quality.
How is standard deviation used in real life?
SD is used in finance (risk assessment), quality control (process consistency), science (experimental reliability), education (grade distribution), and weather (temperature variability).
Is this standard deviation calculator free?
Yes, completely free with no sign-up. All calculations happen in your browser — your data is never sent to any server.