Standard Deviation Calculator

Unlock the Power of Standard Deviation in Your Data

Welcome to our cutting-edge Standard Deviation Calculator – your go-to tool for quick and accurate statistical analysis. Whether you're a student tackling complex datasets, a researcher analyzing experimental results, or a financial analyst crunching market numbers, our calculator simplifies the process of understanding data dispersion.

Standard deviation is the key to unlocking insights about data variability. It tells you how spread out your numbers are from the average (mean). A low standard deviation suggests your data points cluster tightly around the mean, while a high standard deviation indicates they're more scattered. This crucial metric helps you:

Assess data reliability and consistency
Compare different datasets effectively
Make informed decisions based on data spread
Identify outliers and unusual patterns

Our user-friendly calculator does the heavy lifting for you. Simply input your numbers, and we'll instantly compute the mean, variance, and standard deviation. No more manual calculations or complex formulas – get precise results in seconds!

Enter your data points (comma-separated):

Your Results:

Mean (Average):

Variance:

Standard Deviation:

Why Choose Our Standard Deviation Calculator?

Lightning-fast calculations for datasets of any size
User-friendly interface – no statistical expertise required
Precise results to four decimal places
Free to use, with no registration needed
Perfect for students, professionals, and researchers alike

Start exploring your data's hidden patterns today. Whether you're analyzing exam scores, financial returns, scientific measurements, or any other numerical dataset, our Standard Deviation Calculator is your trusted companion for insightful statistical analysis.

Step 1: Calculate the Mean

Add up all the numbers in your dataset and divide by the count of numbers.

Formula: μ = (Σx) / N
Where μ is the mean, Σx is the sum of all values, and N is the number of values.

Step 2: Calculate the Variance

For each number: subtract the Mean and square the result. Then find the average of those squared differences.

Formula: σ² = Σ(x - μ)² / (N - 1)
Where σ² is the variance, x represents each value, μ is the mean, and N is the number of values.

Step 3: Calculate the Standard Deviation

Take the square root of the variance.

Formula: σ = √σ²
Where σ is the standard deviation and σ² is the variance.

Example Calculation

Dataset: 2, 4, 4, 4, 5, 5, 7, 9

Mean:
(2 + 4 + 4 + 4 + 5 + 5 + 7 + 9) / 8 = 5
Variance:
[(2-5)² + (4-5)² + (4-5)² + (4-5)² + (5-5)² + (5-5)² + (7-5)² + (9-5)²] / 7
= (9 + 1 + 1 + 1 + 0 + 0 + 4 + 16) / 7
= 32 / 7 ≈ 4.57
Standard Deviation:
√4.57 ≈ 2.14

Standard Deviation Calculator: Simplify Your Data Analysis