Sigma Symbol (Σ, σ): Summation, Standard Deviation and LaTeX

The sigma symbol is Σ in uppercase and σ in lowercase. Uppercase Σ means “add all of these up”. Lowercase σ almost always means standard deviation in statistics, or stress in engineering. Copy either below, or jump to how to type it.

Copy and paste: click either card above to copy the character to your clipboard — Σ for summation and uppercase use, σ for standard deviation. Both paste cleanly into Word, Google Docs, Slack and any modern editor.

Σ is not the same character as ∑

This trips up more people than anything else about sigma. There are two visually similar characters and they are not interchangeable:

The summation operator is taller and gets extra spacing from limits above and below. Word’s equation editor and LaTeX both insert the correct one automatically, so you rarely need to pick by hand — but if you paste a formula out of a PDF, check which one you got.

Σ as summation

The index below the sigma says where to start, the value above says where to stop, and the expression to the right is what gets added:

An arithmetic series has a closed form worth memorising:

Sums nest, and the index can run over a set rather than a range:

σ as standard deviation

Lowercase sigma is the population standard deviation — the square root of the variance, and a measure of how far values sit from the mean:

It also sets the width of the normal distribution, which is where the 68–95–99.7 rule comes from:

Other meanings of σ

• Mechanics — stress, force per unit area: σ = F/A
• Electromagnetism — electrical conductivity, or surface charge density
• Thermodynamics — the Stefan–Boltzmann constant
• Chemistry — a sigma bond, the head-on overlap of two orbitals
• Manufacturing — Six Sigma, meaning six standard deviations between the mean and the nearest specification limit

How to type the sigma symbol

Windows

• Uppercase Σ: Alt + 228 on the numeric keypad
• Lowercase σ: Alt + 229
• In Word, type 03C3 then Alt + X for σ, or 2211 then Alt + X for the ∑ operator

Mac

• Option + W gives ∑, the summation operator — not the Greek letter
• For the letter, open Character Viewer with Control + Command + Space and search “sigma”

HTML

• Σ for Σ, σ for σ
• ∑ for the ∑ operator

The sigma symbol in LaTeX

LaTeX keeps the letter and the operator strictly separate, which is the main thing to learn here. \Sigma is the letter; \sum is the operator that takes limits:

In a displayed equation the limits sit above and below automatically. Inline, they move beside the symbol to keep line spacing even — force the displayed style with \limits if you need it:

Frequently asked questions

What does Σ mean in maths?

Add everything up. The index below gives the starting value, the number above the stopping value, and the expression to the right is the term being summed.

What does σ mean in statistics?

The population standard deviation — the square root of the variance. A larger σ means the data is more spread out around the mean.

Why are there two lowercase sigmas?

Greek writes σ inside a word and ς at the end of one. Mathematics only ever uses σ.

See also our guide to integrals and summations in LaTeX, the omega symbol and the alpha symbol.

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