Standard Deviation Calculator
Calculate the standard deviation and variance of a dataset from summary statistics. Supports both population and sample standard deviation with Bessel's correction for unbiased estimation.
This free online standard deviation calculator provides instant results with no signup required. All calculations run directly in your browser — your data is never sent to a server. Enter your values below and see results update in real time as you type. Perfect for everyday calculations, homework, or professional use.
The sum of all data values in your dataset.
The sum of each data value squared.
Total number of data points.
How to Use This Calculator
Enter your input values
Fill in all required input fields for the Standard Deviation Calculator. Most fields include unit selectors so you can work in your preferred unit system — metric or imperial, whichever matches your problem.
Review your inputs
Double-check that all values are correct and that you have selected the right units for each field. Incorrect units are the most common source of calculation errors and can produce results that are off by factors of 2, 10, or more.
Read the results
The Standard Deviation Calculator instantly computes the output and displays results with units clearly labeled. All calculations happen in your browser — no loading time and no data sent to a server.
Explore parameter sensitivity
Try adjusting individual input values to see how the output changes. This is a quick and effective way to develop intuition about how different parameters influence the result and to identify which inputs have the largest effect.
Formula Reference
Standard Deviation Calculator Formula
See calculator inputs for the governing equation
Variables: All variables and their units are labeled in the calculator interface above. Input fields accept values in multiple unit systems — select your preferred unit from the dropdown next to each field.
When to Use This Calculator
- •Use the Standard Deviation Calculator when you need accurate results quickly without the risk of manual computation errors or unit conversion mistakes.
- •Use it to verify calculations made by hand or in spreadsheets — an independent check can catch errors before they lead to costly decisions.
- •Use it to explore how changing input parameters affects the output — a quick way to develop intuition and identify the most influential variables.
- •Use it when collaborating with others to ensure everyone is working from the same numbers and applying the same assumptions.
About This Calculator
The Standard Deviation Calculator is a free, browser-based calculation tool for engineers, students, and technical professionals. Calculate the standard deviation and variance of a dataset from summary statistics. Supports both population and sample standard deviation with Bessel's correction for unbiased estimation. It implements standard formulas and supports both metric (SI) and imperial unit systems with automatic unit conversion. All calculations are performed instantly in your browser with no data sent to a server. Use this calculator as a quick reference and sanity-check tool during design, analysis, and learning. Always verify results against primary engineering references and applicable standards for any safety-critical application.
About Standard Deviation Calculator
The standard deviation calculator measures the amount of dispersion or spread in a dataset. A low standard deviation means data points cluster near the mean, while a high standard deviation indicates wide spread. Standard deviation is the most commonly used measure of variability in statistics, finance, quality control, and the natural sciences. This calculator computes both the population standard deviation (when your data represents the entire population) and the sample standard deviation (when your data is a sample from a larger population, using Bessel's correction with n-1 in the denominator). It also reports the corresponding variances and the mean.
The Math Behind It
Formula Reference
Population Standard Deviation
sigma = sqrt(sum((x_i - mu)^2) / N)
Variables: sigma = population std dev; x_i = each value; mu = population mean; N = population size
Sample Standard Deviation
s = sqrt(sum((x_i - x_bar)^2) / (n - 1))
Variables: s = sample std dev; x_bar = sample mean; n = sample size; n-1 = Bessel's correction
Worked Examples
Example 1: Test scores
Five test scores: 60, 70, 70, 80, 70. Find the sample standard deviation.
The sample standard deviation is approximately 7.07 points.
Example 2: Manufacturing measurements
Bolt diameters (mm): 10.1, 10.0, 9.9, 10.0, 10.0. Calculate population standard deviation.
The population standard deviation is 0.063 mm, indicating tight dimensional control.
Common Mistakes & Tips
- !Using the population formula (dividing by n) when working with a sample, which underestimates variability.
- !Confusing standard deviation with standard error. Standard error = s/sqrt(n) and measures uncertainty in the mean, not data spread.
- !Forgetting that standard deviation cannot be negative; if you get a negative value, check your computation.
Related Concepts
Used in These Calculators
Calculators that build on or apply the concepts from this page:
Frequently Asked Questions
When do I use population vs. sample standard deviation?
Use population standard deviation when your data includes every member of the population. Use sample standard deviation when your data is a subset drawn from a larger population, which is the more common scenario in practice.
What is Bessel's correction?
Bessel's correction divides by (n-1) instead of n when computing sample variance. This corrects the bias that arises because the sample mean is used in place of the unknown population mean.
Can standard deviation be zero?
Yes, a standard deviation of zero means all data values are identical. There is no spread at all.