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Standard Deviation Calculator

Calculate population and sample standard deviation, variance, mean, and coefficient of variation. See step-by-step statistics for your data set. Free tool for students and analysts.

Last revised 2 September 2026

By Team GlobalCalqulate · About our editorial standards

Data

Data Values (comma separated)

Enter numbers separated by commas.

Calculation Type

Standard Deviation

5.2372

Mean: 18.00 | n=8

Methodology

Formula:: Mean
Content last updated:: September 2026
Scheduled re-verification:: September 2027

Calculation type: Exact calculation.

How to Use This Calculator

Enter Your Data

Type or paste your numbers, separated by commas. The calculator accepts whole numbers and decimals.

Choose Sample or Population

Sample (n-1) is for a subset of data and gives an unbiased estimate. Population (n) is for complete data sets where you have every value.

Review Statistics

See standard deviation, variance, mean, coefficient of variation, and range — a complete summary of your data set.

Formula & methodology

Formula used

Mean

x̄ = Σxᵢ / n

The arithmetic average of the values you enter.

Variance

s² = Σ(xᵢ − x̄)² / (n − 1)   [sample]     σ² = Σ(xᵢ − x̄)² / n   [population]

Each value's distance from the mean is squared, then averaged. The sample form divides by n − 1 (Bessel's correction) because a sample's own mean sits closer to its own points than the true population mean does, which would otherwise understate the spread.

Standard deviation

s = √s²

The square root of the variance, which returns the figure to the original units.

Coefficient of variation

CV = (s ÷ x̄) × 100

Spread expressed as a percentage of the mean, so data sets with different units can be compared.

Variable definitions

Symbol	Meaning	Unit
xᵢ	Each value. one data point from your set	—
n	Count. how many values you entered	count
x̄	Mean. the arithmetic average	—

Step-by-step calculation

1. Enter your values
Comma-separated; at least two values are needed for a standard deviation.
2. Choose sample or population
Sample (n − 1) for a subset; population (n) only when you hold every value.
3. Read the spread
Variance, standard deviation and coefficient of variation are reported together.

Limitations

Standard deviation assumes the values are comparable measurements on one scale. Mixing units, or including a value entered in error, moves the result substantially because differences are squared.
It is sensitive to outliers for that same reason. A single extreme value can dominate the result — the interquartile range is more robust when outliers are expected.
The 68 / 95 / 99.7 rule quoted for standard deviations applies to a normal distribution. For skewed or bimodal data those percentages do not hold.

This page is educational. It applies the formula described above to the figures you enter and shows the arithmetic behind the result. The output is only as good as the inputs and the assumptions listed here, and it is general information rather than advice about your particular situation.

Help & FAQs

Frequently Asked Questions

Clear answers to common questions to help you use this calculator confidently.

What is standard deviation?

Tap to view the answer

Standard deviation measures how spread out numbers are from the mean. A low SD means numbers are close to the mean; a high SD means they're widely scattered.

What's the difference between population and sample SD?

Tap to view the answer

Population SD divides by n (all data). Sample SD divides by n−1 (Bessel's correction) for unbiased estimation when your data is a sample rather than a complete population.

What is variance?

Tap to view the answer

Variance is the average of squared differences from the mean. Standard deviation is the square root of variance, expressed in the same units as your original data.

What is coefficient of variation?

Tap to view the answer

CV = (SD / Mean) × 100%. It measures relative variability independent of the unit of measurement, useful for comparing spread across data sets with different scales.

How do I interpret standard deviation?

Tap to view the answer

In a normal distribution, about 68% of data falls within 1 SD of the mean, ~95% within 2 SD, and ~99.7% within 3 SD — this is known as the empirical rule.

Need more help? Contact support or email globalcalqulate@gmail.com

We typically reply within 24–48 hours.

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How to Use This Calculator

Enter Your Data

Type or paste your numbers, separated by commas. The calculator accepts whole numbers and decimals.

Choose Sample or Population

Sample (n-1) is for a subset of data and gives an unbiased estimate. Population (n) is for complete data sets where you have every value.

Review Statistics

See standard deviation, variance, mean, coefficient of variation, and range — a complete summary of your data set.

Understanding Your Results

Standard Deviation
A measure of how spread out numbers are from the mean. Low SD = data points cluster near the mean. High SD = data is widely scattered.
Sample vs Population
Sample divides by (n-1) using Bessel's correction for unbiased estimation from a subset. Population divides by n when you have all data points.
Coefficient of Variation
CV = (SD ÷ Mean) × 100%. Measures relative variability — useful for comparing data sets with different units or means.
Variance
The average of squared differences from the mean. SD is the square root of variance. Both measure spread, but SD is in the original units.

Key Tips

✓
Use sample (n-1) when working with a subset of a larger population — this gives an unbiased estimate.
✓
Use population (n) only when you have every possible data point.
✓
In a normal distribution: ~68% within 1 SD, ~95% within 2 SD, ~99.7% within 3 SD of the mean.
✓
CV is useful for comparing variability across different data sets — a CV under 10% indicates low relative variability.

How Standard Deviation Works

What Standard Deviation Tells You

Standard deviation answers: how typical is the average? In a class where all students score 70-75 on a test, the SD is small (~2). In a class where scores range from 40 to 100, the SD is large (~20). The larger the SD, the less representative the mean is of any individual data point. Financial analysts use SD to measure investment volatility. Quality control engineers use it to monitor manufacturing consistency.

Sample vs Population — Why n-1 Matters

When you calculate SD from a sample (not the entire population), dividing by n underestimates the true population SD. Bessel's correction (dividing by n-1) compensates for this bias. The difference matters most with small samples. With n=5, sample SD uses n-1=4 (25% difference). With n=100, the correction is only 1%. Use population SD when you have census data; use sample SD when you have survey data.

Coefficient of Variation — Comparing Apples to Oranges

CV = (SD ÷ Mean) × 100%. It expresses variability relative to the mean, making it unit-independent. You can compare the variability of heights (inches) to weights (pounds), or stock A ($50 mean, $5 SD) to stock B ($500 mean, $50 SD). Both have CV=10% — they're equally volatile relative to their price. CV is widely used in finance, quality control, and laboratory testing.

Formula & methodology

Formula used

Mean

x̄ = Σxᵢ / n

The arithmetic average of the values you enter.

Variance

s² = Σ(xᵢ − x̄)² / (n − 1)   [sample]     σ² = Σ(xᵢ − x̄)² / n   [population]

Standard deviation

s = √s²

The square root of the variance, which returns the figure to the original units.

Coefficient of variation

CV = (s ÷ x̄) × 100

Spread expressed as a percentage of the mean, so data sets with different units can be compared.

Variable definitions

Symbol	Meaning	Unit
xᵢ	Each value. one data point from your set	—
n	Count. how many values you entered	count
x̄	Mean. the arithmetic average	—

Step-by-step calculation

1. Enter your values
Comma-separated; at least two values are needed for a standard deviation.
2. Choose sample or population
Sample (n − 1) for a subset; population (n) only when you hold every value.
3. Read the spread
Variance, standard deviation and coefficient of variation are reported together.

Limitations

Standard deviation assumes the values are comparable measurements on one scale. Mixing units, or including a value entered in error, moves the result substantially because differences are squared.
It is sensitive to outliers for that same reason. A single extreme value can dominate the result — the interquartile range is more robust when outliers are expected.
The 68 / 95 / 99.7 rule quoted for standard deviations applies to a normal distribution. For skewed or bimodal data those percentages do not hold.

Calculator inputs

Data

Your results

Methodology

How to Use This Calculator

Formula & methodology

Formula used

Mean

Variance

Standard deviation

Coefficient of variation

Variable definitions

Step-by-step calculation

Limitations

What is standard deviation?

What's the difference between population and sample SD?

What is variance?

What is coefficient of variation?

How do I interpret standard deviation?

Related calculators

More everyday calculators

Calculator inputs

Data

Your results

Methodology

How to Use This Calculator

Example: 8 Data Points

Understanding Your Results

Key Tips

How Standard Deviation Works

What Standard Deviation Tells You

Sample vs Population — Why n-1 Matters

Coefficient of Variation — Comparing Apples to Oranges

Formula & methodology

Formula used

Mean

Variance

Standard deviation

Coefficient of variation

Variable definitions

Step-by-step calculation

Limitations

Example: 8 Data Points

Understanding Your Results

Key Tips

How Standard Deviation Works

What Standard Deviation Tells You

Sample vs Population — Why n-1 Matters

Coefficient of Variation — Comparing Apples to Oranges