Standard Deviation Calculator
Enter your data below and choose whether you want sample or population standard deviation. Values can be separated by commas, spaces, or new lines.
Tip: Sample standard deviation is usually used when your values are a subset of a larger group.
What is standard deviation?
Standard deviation measures how spread out your numbers are around the mean (average). If your values are tightly clustered, the standard deviation is small. If your values vary a lot, the standard deviation is larger.
In practical terms, it tells you how much variation exists in your dataset. That makes it useful for statistics, finance, data science, quality control, and research.
How to use this calculator
Step 1: Enter data points
Type or paste your numbers into the input box. You can separate values with:
- Commas (for example,
10, 15, 20) - Spaces (for example,
10 15 20) - New lines (one number per line)
Step 2: Choose sample or population
- Sample standard deviation: divides by
n - 1. Use this when data is a sample from a larger population. - Population standard deviation: divides by
n. Use this when data includes the full population.
Step 3: Click Calculate
The tool returns your count, mean, variance, and standard deviation instantly.
Formulas used
Population standard deviation
σ = √( Σ(x - μ)² / n )
Where μ is the population mean and n is the number of values.
Sample standard deviation
s = √( Σ(x - x̄)² / (n - 1) )
Where x̄ is the sample mean. The n - 1 adjustment (Bessel’s correction) helps reduce bias when estimating population variability from a sample.
Why this matters
Standard deviation is one of the most important descriptive statistics because it helps you understand consistency and risk:
- Investing: compare volatility of returns.
- Education: measure score dispersion across students.
- Manufacturing: track process consistency.
- Science: assess the spread of experimental results.
Common mistakes to avoid
- Using population formula when you really have a sample.
- Entering non-numeric characters in your data.
- Interpreting standard deviation without considering the mean and context.
Quick example
Suppose your values are 4, 8, 6, 5, 3. The mean is 5.2. When you compute squared differences and take the square root of variance, you get a standard deviation that summarizes the typical distance from the mean.
This calculator performs those steps automatically and shows the results clearly.
FAQ
Can standard deviation be negative?
No. Variance and standard deviation are always zero or positive.
What does a standard deviation of zero mean?
All values are identical, so there is no spread.
Do outliers affect standard deviation?
Yes. Outliers can increase standard deviation significantly because the formula squares differences from the mean.