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∏

n-ary product

N-ary product

∏ is the product sign, also called big pi notation. It tells you to multiply a whole run of terms, the same way Σ tells you to add them up. You see it in factorials, products over prime numbers and probability formulas. It looks like the Greek capital letter Π, but Unicode encodes it as a separate maths operator.

Text symbol

What ∏ means

Multiply every term the indices select. In ∏ᵢ₁ⁿ aᵢ, the small i is a counter. It runs from 1 up to n, so the expression means a₁ a₂ … aₙ. The product sign packs a long chain of multiplications into one operator and states the range exactly. For example, n! (n factorial) is the product of k for k from 1 to n.

Who introduced the sign is disputed. One account credits René Descartes, while the historian Florian Cajori points to Carl Friedrich Gauss's use in 1812. The sign was developed as a partner to Σ, the notation for repeated addition.

Formal mathematical notation. Writing it signals indexed multiplication inside a formula.

Part of collections

➗

Math Symbols

Greek Letters

Don't confuse it with

Greek Capital Letter Pi

Π is the Greek capital letter pi, used in words and as a variable name. ∏ is the product operator. In LaTeX, \Pi gives Π and \prod gives ∏.

Cyrillic Capital Letter Pe

П is the Cyrillic capital letter Pe, used in Russian and other words. ∏ is the large product operator.

Combination ideas

Multiply all the xᵢ together.

Product of 1 through n is n factorial.

Euler product over primes; equals the zeta function ζ(s).

Questions people ask

Why does ∏ show as a box on some devices?

Because that device's fonts have no glyph for it. The character is still correct and still copies correctly — the box is a missing glyph, not a broken character.

How to type or find ∏

Also called: product sign · product operator · big pi
Search it as: prod · pi product notation · capital pi product
Shows up in: Anything that takes text · its shape is whatever your font draws

Windows (Word)

⎇Alt+XType 220F, then AltX to get ∏.

Windows

⊞Win+Rrun charmap for the full table, or use the emoji picker's Ω symbols tab (Win .).

macOS

⌃Control+⌘Command+␣SpaceOpen the character viewer and search “n-ary product”.

Linux

⎈Ctrl+⇧Shift+UType 220f, then Enter or Space.

HTML

∏

CSS

\220F

LaTeX

In math mode, type \prod. Add limits with _ and , as in \prod_{i1}n.

Codes and encoding1 code points

HTML decimal

∏

HTML hex

∏

CSS content

content: "\220F";

Each escape is closed by the next backslash; a trailing space is needed before a literal hex digit.

URL encoded

%E2%88%8F

On screen

Code points

JS .length

UTF-8 bytes

A visible symbol can contain several code points. JS .length counts UTF-16 units; UTF-8 counts bytes.

Families this belongs to

Maths & numbers1,835 symbols

1️⃣📏📐✖️➕➖➗🟰♾️#️⃣*️⃣0️⃣