Standard Deviation Calculator

Calculate standard deviation and variance for any dataset instantly. Our free tool handles both sample and population formulas, providing clear results and visualizations to help you understand your data's spread.

Standard Deviation Calculator

Calculate standard deviation, variance, and other descriptive statistics for your dataset.

Enter Data

Enter at least 2 numbers for sample standard deviation

Sample Standard Deviation (n-1)Population Standard Deviation (n)

How the Standard Deviation Calculator Works

Enter your data as comma-separated numbers, space-separated values, or paste directly from a spreadsheet. The calculator accepts any format and extracts the numbers automatically.

Choose between sample standard deviation (divides by n-1) or population standard deviation (divides by n). Sample is used when your data represents a subset of a larger population. Population is used when you have all data points.

Results display count, mean, median, standard deviation, variance, minimum, maximum, and range. The step-by-step section shows how the mean, variance, and standard deviation were calculated from your data.

When You'd Actually Use This

Analyzing test score distributions

Your class scored 78, 82, 85, 90, 95 on an exam. Calculate standard deviation to see how spread out the scores are around the average.

Quality control in manufacturing

Measure 20 parts from production. Low standard deviation means consistent manufacturing. High deviation indicates process problems needing attention.

Investment risk assessment

Compare standard deviation of stock returns. Higher deviation means more volatility and risk. Use this to balance your portfolio's risk level.

Scientific experiment analysis

Run multiple trials of your experiment. Standard deviation shows measurement precision. Small deviation means your method is repeatable.

Survey data interpretation

Analyze responses from a sample group. Standard deviation helps you understand if responses cluster around the mean or vary widely.

Statistics homework problems

Your assignment gives a dataset and asks for standard deviation. Enter the values and verify your manual calculation step by step.

What to Know Before Using

Sample vs population matters.Sample standard deviation uses n-1 (Bessel's correction) to give an unbiased estimate. Population uses n. Sample is more common since you rarely have complete population data.

Standard deviation has the same units as data.If your data is in meters, standard deviation is in meters. Variance is in squared units (meters²), which is harder to interpret directly.

Outliers inflate standard deviation.A single extreme value can dramatically increase the standard deviation. Check your data for outliers before interpreting spread.

Zero standard deviation means identical values.If every data point equals the mean, standard deviation is zero. This indicates no variation in your dataset.

Pro tip: For normal distributions, 68% of data falls within one standard deviation of the mean, 95% within two, and 99.7% within three. This "68-95-99.7 rule" helps interpret your results.

Common Questions

When should I use sample vs population?

Use sample when your data is a subset of a larger group (survey respondents, test products). Use population when you have every member (all employees, complete census).

What does a high standard deviation mean?

High standard deviation means data points are spread far from the mean. There's high variability. Low standard deviation means data clusters tightly around the average.

Can standard deviation be negative?

No. Standard deviation is the square root of variance, which is always positive or zero. You can't have negative spread in data.

How many data points do I need?

Technically two for sample standard deviation. Practically, 30+ gives more reliable estimates. With fewer than 10 points, the standard deviation itself has high uncertainty.

What's the difference between variance and standard deviation?

Variance is the average squared deviation from the mean. Standard deviation is the square root of variance. Standard deviation is more interpretable because it's in original units.

Does this handle negative numbers?

Yes. Negative values work fine. Temperature readings, financial losses, or any data with negative values calculate correctly.

How is median different from mean?

Mean is the arithmetic average. Median is the middle value when sorted. Median is less affected by outliers. Both measure central tendency but answer different questions.

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