Is this standard deviation calculator free?

Yes, this SD calculator is 100% free with no registration required. Use it unlimited times for homework, research, or data analysis.

Standard Deviation Calculator - Free SD Calculator Online

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Population standard deviation (divide by n instead of n-1)

What is Standard Deviation?

Standard deviation measures the amount of variation or dispersion in a set of values. A low standard deviation indicates that values tend to be close to the mean, while a high standard deviation indicates that values are spread out over a wider range.

Standard Deviation Formulas

Sample Standard Deviation

s = √[Σ(x - x̄)² / (n - 1)]

Use this when your data represents a sample from a larger population.

Population Standard Deviation

σ = √[Σ(x - μ)² / N]

Use this when your data represents the entire population.

Understanding the Results

68% of data falls within 1 standard deviation of the mean
95% of data falls within 2 standard deviations
99.7% of data falls within 3 standard deviations

This is known as the Empirical Rule or 68-95-99.7 Rule for normally distributed data.

Sample vs. Population

Choose Sample when:

Your data is a subset of a larger group
You want to estimate the population variability
Most practical applications

Choose Population when:

You have data for the entire group
You’re calculating for a complete, finite dataset

Frequently Asked Questions

How do I calculate standard deviation?

To calculate standard deviation: (1) Find the mean of your data, (2) Subtract the mean from each value to get deviations, (3) Square each deviation, (4) Find the mean of squared deviations (divide by n-1 for sample, n for population), (5) Take the square root. Or simply enter your data in our calculator above!

What is the difference between sample and population standard deviation?

Sample standard deviation (s) divides by n-1 (called Bessel’s correction) because samples tend to underestimate population variability. Population standard deviation (σ) divides by N because you have all the data. For most real-world applications, use sample SD.

What is a “good” standard deviation?

There’s no universal “good” standard deviation—it depends entirely on your context and what you’re measuring. A SD of 5 might be small for house prices but large for exam scores. Compare SD to the mean using the coefficient of variation (CV = SD/mean × 100%) for relative comparisons.

What does standard deviation tell you?

Standard deviation tells you how spread out values are from the average. A small SD means values cluster tightly around the mean (consistent data). A large SD means values are widely spread (variable data). It’s the most common measure of variability.

What is variance vs standard deviation?

Variance is the average of squared deviations from the mean. Standard deviation is the square root of variance. SD is preferred because it’s in the same units as your data, making it easier to interpret. Variance = SD².

How does standard deviation relate to the normal distribution?

For normally distributed data, the 68-95-99.7 rule applies: 68% of data falls within ±1 SD of the mean, 95% within ±2 SD, and 99.7% within ±3 SD. This makes SD useful for identifying outliers and understanding data spread.

When should I use standard deviation vs. range?

Standard deviation uses all data points and is more stable than range (which only uses min and max). Use SD for formal analysis and when you need a precise measure of spread. Use range for quick, rough estimates or very small samples.

Mean Calculator - Calculate the average
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Variance Calculator - Full descriptive statistics
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