The Standard Deviation Calculator helps you quickly measure how spread out a set of numbers is from the average (mean). It’s a useful tool in statistics, research, and data analysis to understand variability in your dataset.
Standard Deviation Calculator
Enter numbers separated by commas, spaces or new lines (or add numbers one-by-one).
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📊 How to Use the Standard Deviation Calculator (Free & Pro)
The Standard Deviation Calculator helps you measure how spread out numbers are in a dataset. It calculates both population and sample standard deviation instantly, making it ideal for students, data analysts, and researchers who need quick, accurate statistical insights.
Use it to understand variability in data, detect outliers, or assess consistency in your measurements.
- Enter your data: Add a list of numbers separated by commas (e.g., 2, 4, 4, 4, 5, 5, 7, 9).
- Select calculation type: Choose between Sample or Population standard deviation.
- Click Calculate: The calculator displays mean, variance, and standard deviation instantly.
- Reset: Clears inputs for a new calculation.
💡 Example: For data 2, 4, 4, 4, 5, 5, 7, 9, the mean = 5, and standard deviation ≈ 2.
Formula for Population Standard Deviation (σ):
σ = √[ Σ(xᵢ − μ)² / N ]
Formula for Sample Standard Deviation (s):
s = √[ Σ(xᵢ − x̄)² / (n − 1) ]
Where:
- σ or s = standard deviation
- xᵢ = individual data points
- μ or x̄ = mean (average)
- N or n = number of data points
- 📤 Export full statistical summary (mean, variance, deviation, range) as PDF/CSV
- 📊 Interactive charts & data distribution visualization
- 🧠 Advanced mode for weighted or grouped data
- ⚙️ Supports large datasets (1000+ values)
💎 Available in Standard Deviation Calculator Pro.
- Data: 10, 12, 23, 23, 16, 23, 21, 16 → SD ≈ 4.90
- Data: 4, 4, 4, 4 → SD = 0 (no variation)
- Data: 2, 4, 4, 4, 5, 5, 7, 9 → SD ≈ 2
📈 The higher the standard deviation, the more spread out the data.
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Open ToolStandard Deviation Calculator – Mean, Variance & Data Spread Tool
Use our free Standard Deviation Calculator to find the standard deviation, variance, and mean of a data set. This calculator helps you understand how spread out your numbers are — whether you’re analyzing test scores, investments, or scientific data.
What Is Standard Deviation?
Standard deviation (σ or SD) is a statistical measure that shows how much the values in a data set deviate from the mean (average). A low standard deviation means the numbers are close to the mean, while a high deviation indicates more variability.
Formula for Standard Deviation
Population Standard Deviation:
σ = √( Σ (xᵢ − μ)² / N )
Sample Standard Deviation:
s = √( Σ (xᵢ − x̄)² / (n − 1) )
Where:
- xᵢ = each value
- μ = population mean
- x̄ = sample mean
- N = number of data points (population)
- n = number of data points (sample)
How to Use the Standard Deviation Calculator
- Enter your data values separated by commas.
- Select whether you are using a sample or population.
- Click “Calculate” to see the mean, variance, and standard deviation.
- Use results to understand the data spread or consistency.
Example Calculation
Data Set: 2, 4, 6, 8, 10
| Value (x) | x − Mean (x − 6) | (x − Mean)² |
|---|---|---|
| 2 | -4 | 16 |
| 4 | -2 | 4 |
| 6 | 0 | 0 |
| 8 | 2 | 4 |
| 10 | 4 | 16 |
| Sum of (x − Mean)² = 40 | Variance = 8 | |
Standard Deviation = √8 = 2.83
When to Use Standard Deviation
- Statistics: Measure variability in surveys or experiments.
- Finance: Assess risk or volatility of investments.
- Education: Analyze consistency of test scores.
- Science & Research: Evaluate accuracy in repeated experiments.
Interpreting Standard Deviation
- Low SD: Data values are closely grouped (stable, consistent results).
- High SD: Data values are spread out (high variability).
Frequently Asked Questions (FAQ)
1. What is a good standard deviation?
It depends on the context. In finance, a low SD means stable returns; in science, it means precise measurements.
2. What’s the difference between population and sample SD?
Population SD uses all data points (divided by N), while sample SD uses a subset (divided by n−1).
3. Can I calculate variance from standard deviation?
Yes, variance = (standard deviation)².
4. Can this calculator handle decimals and negatives?
Yes! You can enter any numeric data, including negative or decimal values.
Final Thoughts
The Standard Deviation Calculator helps you analyze data variability easily. It’s ideal for students, researchers, and analysts who need to measure how consistent or spread out their data is — fast, accurate, and free.
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WHO – Data & Statistics Info