Standard Deviation Calculator: Measure Data Spread

Standard deviation is one of the most important concepts in statistics. It tells you how spread out your data is from the average.

What Is Standard Deviation?

Standard deviation (σ) measures the amount of variation or dispersion in a set of values. A low standard deviation means values are close to the mean; a high one means they're spread out.

How to Calculate Standard Deviation

Step 1: Find the mean (average) of your data

Step 2: Subtract the mean from each value and square the result

Step 3: Find the average of those squared differences (this is the variance)

Step 4: Take the square root of the variance

Example: Test Scores

Scores: 85, 92, 78, 95, 88

1. Mean = (85+92+78+95+88) ÷ 5 = 87.6

2. Differences: (85-87.6)²=6.76, (92-87.6)²=19.36, (78-87.6)²=92.16, (95-87.6)²=54.76, (88-87.6)²=0.16

3. Variance = (6.76+19.36+92.16+54.76+0.16) ÷ 5 = 34.64

4. Standard Deviation = √34.64 = 5.89

This means most scores fall within ±5.89 points of the mean (81.7 to 93.5).

Population vs Sample

• Population SD: Divide by N (all data points)
• Sample SD: Divide by N-1 (when data is a sample of a larger population)

Our calculator supports both!

Using Our Standard Deviation Calculator

Our Standard Deviation Calculator makes it easy:

• Enter any number of values
• See mean, variance, and standard deviation
• Choose between population and sample formulas

💡 Pro Tip: In finance, standard deviation measures investment risk. A stock with a higher standard deviation has more price volatility — and potentially higher returns.

*Calculate standard deviation with our free Statistics Calculator.*