Best Standard Deviation Calculator - Compute in few 1 Sec

Standard Deviation Calculator

Input Data

Enter Numbers

Separate numbers with commas, spaces, or new lines.

Standard Deviation Type

Sample (n-1)

Population (n)

Results

Count (n)

0

Sum

0

Mean (Average)

0

Variance (Sample)

0

Standard Deviation (Sample)
0

Variance (Population)

0

Standard Deviation (Population)
0

Enter your data and click "Calculate Standard Deviation" to see results.

Sample Standard Deviation Formula

s = √[Σ(xi - x̄)² / (n - 1)]

Where:

s = sample standard deviation

xi = each value in the dataset

x̄ = sample mean (average)

n = number of values in the sample

Σ = summation (add up all values)

Population Standard Deviation Formula

σ = √[Σ(xi - μ)² / n]

Where:

σ = population standard deviation

xi = each value in the dataset

μ = population mean (average)

n = number of values in the population

Σ = summation (add up all values)

Frequently Asked Questions - Standard Deviation Calculator

What is standard deviation?

Standard deviation is a statistical measure that shows how much variation or dispersion exists from the average (mean) in a set of data. A low standard deviation means the data points are close to the mean, while a high standard deviation indicates the data is spread out over a wider range of values.

How do I use the standard deviation calculator?

Simply enter your numbers separated by commas or spaces into the input field, select whether you want sample or population standard deviation, and click “Calculate.” The Standard Deviation Calculator will instantly display the results including mean, variance, and standard deviation.

What's the difference between sample and population standard deviation?

Population standard deviation (σ) is used when you have data for the entire population
Sample standard deviation (s) is used when you have data from a sample of a larger population and uses (n-1) in the denominator for better estimation

Which should I use - sample or population?

Use sample standard deviation if your data represents a subset of a larger group (most common in research and statistics). Use population standard deviation only if you have data for the entire population you’re studying.

Why does sample standard deviation divide by (n-1) instead of n?

Dividing by (n-1) instead of n is called Bessel’s correction. It provides an unbiased estimate of population variance when working with sample data, compensating for the fact that sample variance tends to underestimate population variance.

What format should I enter my numbers in?

You can enter numbers in Standard Deviation Calculator in several formats:

Comma-separated: 10, 12, 23, 16
Space-separated: 10 12 23 16
Line-separated (one per line)

The calculator automatically handles different formats.

Can I calculate standard deviation for negative numbers?

Yes, the Standard Deviation Calculator works with negative numbers, decimals, and any real numbers. Just enter them the same way as positive numbers.

How many decimal places does the calculator show?

The Standard Deviation Calculator typically displays results rounded to 2-4 decimal places for readability, while maintaining full precision in internal calculations.

What's the minimum number of data points needed?

For population standard deviation, you need at least 1 data point. For sample standard deviation, you need at least 2 data points (since n-1 must be greater than 0).

What is variance?

Variance is the average of the squared differences from the mean. Standard deviation is simply the square root of variance. Variance is measured in squared units, while standard deviation uses the same units as your original data.

What does a standard deviation of 0 mean?

A standard deviation of 0 means all values in your dataset are identical – there is no variation from the mean.

How do I interpret standard deviation results?

Small standard deviation: Data points are clustered close to the mean
Large standard deviation: Data points are spread out over a wide range
Compare to your mean: A standard deviation of 5 is large if your mean is 10, but small if your mean is 1000