Standard Deviation Calculator
Calculate mean, variance, and standard deviation for any dataset — sample or population.
Standard Deviation Calculator
Your Dataset
Enter numbers separated by commas
Statistical Summary
Smart Insights
Personalized takeaways from your numbers.
Real-Life Examples
8 test scores
The Formula Behind It
σ = √(Σ(x−μ)² / N)Variables
- σ = √(Σ(x−μ)² / n)
How It Works
- Enter your data values separated by commas, spaces, or new lines.
- Choose sample (n−1) or population (N) calculation.
- View mean, variance, standard deviation, and range.
- Use insights for data interpretation.
About Standard Deviation Calculator
The Standard Deviation Calculator measures how spread out your data is from the mean — a fundamental statistic in science, finance, quality control, and education. Enter any dataset and instantly compute mean, variance, and standard deviation.
Sample vs Population
Use sample standard deviation (dividing by n−1) when your data is a subset of a larger population — common in surveys and experiments. Use population standard deviation (dividing by N) when you have complete data for the entire group.
Interpreting Results
A low standard deviation means data points cluster close to the mean. A high standard deviation indicates wide spread. In a normal distribution, roughly 68% of values fall within one SD of the mean, 95% within two SDs, and 99.7% within three SDs.
Practical Applications
Analyze test score distributions, measure investment volatility, monitor manufacturing quality control, evaluate experimental results, and complete statistics homework. Pair with our other math tools for comprehensive data analysis.
Frequently Asked Questions
What is standard deviation?
A measure of how spread out numbers are from the mean. Low SD means data clusters near the average.
Sample vs population standard deviation?
Population (N) divides by N. Sample (n-1) divides by n-1 for unbiased estimation — select the appropriate mode.
How do I enter data?
Enter numbers separated by commas, spaces, or new lines.
What is variance?
Variance is the square of standard deviation — average squared distance from the mean.
When is standard deviation used?
In finance (volatility), quality control, scientific research, and any field analyzing data spread.
What is a normal distribution?
In a bell curve, about 68% of data falls within 1 SD of the mean, 95% within 2 SD.
Can I use decimals?
Yes. Enter any valid decimal numbers.
What is the mean?
The arithmetic average — sum of all values divided by count.
Minimum data points needed?
At least 2 values for sample SD. More data gives more reliable statistics.
Is this for students?
Yes. Ideal for homework, research, and quick data analysis.