What is the sum of squares?

The sum of squares (SS) is the sum of each value's squared deviation from the dataset mean. It measures total variability in a dataset and is a key component in ANOVA and regression analysis.

Does this use population or sample variance?

Both are shown. Population variance divides SS by N; sample variance divides by N-1 (Bessel's correction). The standard deviations are the square roots of each variance.

What input formats are accepted?

Numbers can be separated by commas, spaces, semicolons, or newlines. Decimal points and negative values are fully supported.

What is SS used for in ANOVA?

In ANOVA, the total SS is partitioned into SS between groups (explained variance) and SS within groups (residual/error). The ratio of these, adjusted by degrees of freedom, produces the F-statistic.

How many numbers can I enter?

There is no hard limit. The calculation runs in your browser so very large datasets (thousands of values) may take a moment but will complete without sending data to any server.

Sum of Squares Calculator

Name: Sum of Squares Calculator
Availability: InStock
Author: Nham Vu

Enter a list of numbers to instantly get the sum of squares, mean, variance, and standard deviation.

Enter Your Numbers

Numbers (comma, space, or newline separated)

Quick Examples

Enter numbers on the left and press Calculate

Primary Result

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Sum of Squares (SS)

Count (N)

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Mean (x̄)

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Population Variance (σ²)

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Sample Variance (s²)

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Population Std Dev (σ)

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Sample Std Dev (s)

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Deviation Breakdown

Each value's contribution to SS = (xᵢ − x̄)²

#	Value (xᵢ)	xᵢ − x̄	(xᵢ − x̄)²
Total SS			—

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Summary

Enter a list of numbers to instantly get the sum of squares, mean, variance, and standard deviation.

How it works

Enter your numbers separated by commas, spaces, or newlines.
The calculator computes the mean of the dataset.
Each value's deviation from the mean is squared.
All squared deviations are summed to produce the total sum of squares (SS).
Variance and standard deviation are derived from SS and the count of values.

Use cases

Computing SS for one-way or two-way ANOVA tables.
Checking manual calculations in statistics coursework.
Measuring data spread before running a regression model.
Quickly finding variance and standard deviation for a sample dataset.
Verifying statistical software output for sum of squares components.
Analyzing variability in quality-control measurements.

Frequently Asked Questions

Last updated: 2026-06-13 · Reviewed by Nham Vu