Standard Deviation Calculator

Use our free standard deviation calculator to compute population or sample standard deviation, variance, and mean for any data set.

Math

Numbers

Type

Formula

Standard deviation measures the spread of data from the mean. Population divides by N; sample divides by n-1 (Bessel's correction).

σ = √(∑(xᵢ-μ)²/N), s = √(∑(xᵢ-x̄)²/(n-1))

Percentage: The percentage value you want to apply

Number: The original number or value

Result: The calculated result

How It Works

1Enter numbers separated by commas.
2Choose population or sample.
3Click Calculate.

Examples

Population: 10, 20, 30, 40, 50

1.Mean=30
2.Var=200
3.σ=√200≈14.1421

Result: 14.142136

Sample: 10, 20, 30, 40, 50

1.Mean=30
2.Var=250
3.s=√250≈15.8114

Result: 15.811388

Frequently Asked Questions

The square root of variance, measuring data spread.

Population uses N, sample uses n-1 for unbiased estimate.

σ is population std dev; s is sample std dev.

About 68% within 1σ, 95% within 2σ, 99.7% within 3σ of mean.

Std dev is in original units; variance is in squared units.

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CalculateMe Team

Last updated: 2026-07-14

Standard Deviation Calculator

Formula

How It Works

Examples

Population: 10, 20, 30, 40, 50

Sample: 10, 20, 30, 40, 50

Frequently Asked Questions

What is standard deviation?

Population vs sample?

What does σ mean?

68-95-99.7 rule?

Std dev vs variance?

Related Calculators

Standard Deviation Calculator

Formula

How It Works

Examples

Population: 10, 20, 30, 40, 50

Sample: 10, 20, 30, 40, 50

Frequently Asked Questions

What is standard deviation?

Population vs sample?

What does σ mean?

68-95-99.7 rule?

Std dev vs variance?

Related Calculators