Sexvigintillion (symbolically 10⁸¹ in the short scale, or 10¹⁵⁶ in the long scale) is a large number name belonging to the systematic family of “-illion” numbers in the English language. In the short scale, which is the convention used in the United States, Canada, the United Kingdom, and most of the modern English-speaking world, a sexvigintillion is equal to one followed by eighty-one zeros:
1,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000Written in scientific notation, this is 1 × 10⁸¹. The number is rarely encountered in practical contexts, but it holds a certain fascination for students of mathematics and lexicography because of its position near the boundary of physically meaningful quantities.
Etymology
The word is a compound of Latin numerical roots. The prefix sex- means “six,” and viginti means “twenty,” so sexviginti denotes twenty-six. The suffix -illion derives ultimately from the word million, itself an augmentative of the Italian mille (“thousand”), coined in late medieval Italy to mean “a great thousand.” A sexvigintillion is therefore, quite literally, the twenty-sixth member of the -illion series.
This positional logic is the key to the entire naming system. In the short scale, the n-th -illion is defined as 10^(3n+3). Setting n = 26 yields 10^(3 × 26 + 3) = 10⁸¹. The familiar early members of the sequence follow the same rule: million (n = 1) is 10⁶, billion (n = 2) is 10⁹, trillion (n = 3) is 10¹², and so on. Sexvigintillion follows quinvigintillion (10⁷⁸) and precedes septenvigintillion (10⁸⁴).
Short scale and long scale
Like all -illion names, sexvigintillion has two possible values depending on the numbering convention in use. Under the short scale, each successive -illion is a factor of one thousand larger than the previous one, giving the value 10⁸¹ described above. Under the long scale, historically used in continental Europe and formerly in British English, each -illion is a factor of one million larger than the previous, so the n-th -illion equals 10^(6n). By this convention a sexvigintillion is 10^(6 × 26) = 10¹⁵⁶, a vastly larger number. Long-scale systems also interpose “-illiard” names (milliard, billiard, and so on) for the intermediate powers, so 10¹⁵⁹ would be a sexvigintilliard.
Modern English usage overwhelmingly favors the short scale, and dictionaries of large numbers typically list sexvigintillion as 10⁸¹ with a note about the older long-scale value.
History of the naming system
The systematic extension of number names beyond million originates with the French mathematician Nicolas Chuquet, whose 1484 manuscript Triparty en la science des nombres introduced byllion, tryllion, and successive names up to nonyllion. Later writers extended the pattern with Latin prefixes for the teens and tens: decillion, undecillion, duodecillion, and onward through vigintillion (the twentieth -illion) and its compounds. Names such as sexvigintillion arise from attaching a units prefix (sex-) to the tens root (viginti-), the same construction that produces unvigintillion, duovigintillion, trevigintillion, and their siblings.
The scheme was formalized and extended much further in the twentieth century, most notably by John Horton Conway and Allan Wechsler, whose systematic rules (popularized in Conway and Guy’s The Book of Numbers, 1996) generate a well-defined name for every power of one thousand. Under the Conway-Wechsler system, sexvigintillion is the canonical name for 10⁸¹, though the variant spelling sesvigintillion appears in some treatments owing to Latin assimilation rules for the prefix sex- before certain consonants. Dictionaries that include the word at all generally prefer the sexvigintillion form.
Magnitude and physical comparisons
Sexvigintillion sits at an interesting threshold: it is approximately the point at which numbers exceed anything that can be counted in the physical universe. The number of atoms in the observable universe is commonly estimated at between 10⁷⁸ and 10⁸², which places one sexvigintillion at or just beyond the total count of ordinary matter particles in existence. In other words, if every atom in the observable universe were a counting token, there would not be enough of them to reach a sexvigintillion under most estimates.
Some other reference points help situate the magnitude. The number of ways to arrange a standard 52-card deck is about 8 × 10⁶⁷ (roughly a decilliard of arrangements short of relevance here, but thirteen orders of magnitude below 10⁸¹). The estimated number of grains of sand on Earth, about 10¹⁹, and even the number of water molecules in all of Earth’s oceans, about 5 × 10⁴⁶, are utterly negligible by comparison. Conversely, a googol (10¹⁰⁰) exceeds a sexvigintillion by a factor of ten quintillion.
Usage
Sexvigintillion has essentially no application in science, finance, or engineering, where scientific notation is universally preferred for quantities of this size. Its use is confined almost entirely to recreational mathematics, lexicography, vocabulary lists of large numbers, and educational contexts that illustrate the structure of the -illion naming system. It occasionally appears in idle-game and incremental-game software, a genre in which player scores routinely climb through the higher -illions, giving otherwise obscure names like sexvigintillion a small measure of popular currency.
Related terms
The ordinal form is sexvigintillionth, denoting either the fraction 10⁻⁸¹ or position number 10⁸¹ in a sequence. Neighboring names in the short-scale series include quattuorvigintillion (10⁷⁵), quinvigintillion (10⁷⁸), septenvigintillion (10⁸⁴), and octovigintillion (10⁸⁷). The series continues through trigintillion (10⁹³), centillion (10³⁰³), and, under systematic extensions, without bound.