Vigintillion — Definition, Formula & Examples

A vigintillion is an extremely large number equal to

10^{63}

, or 1 followed by 63 zeros, in the American naming system. It is the name for the number in the 21st group of three zeros after 1,000.

In the short scale (used in the United States and modern British English), a vigintillion denotes $10^{63}$ . The name derives from the Latin "viginti" (twenty), following the convention where an $n$ -illion equals $10^{3(n+1)}$ for $n = 20$ .

Key Formula

1 \text{ vigintillion} = 10^{63} = 10^{3(20+1)}

Where:

$63$ = The number of zeros after the 1 in the short-scale system
$20$ = From "viginti" (Latin for twenty), the index used in the naming pattern

Worked Example

Problem: How many zeros does a vigintillion have, and how does it compare to a trillion?

Recall the pattern: In the short scale, an n-illion equals

10^{3(n+1)}

. A trillion is n = 4, so

10^{12}

. A vigintillion is n = 20, so

10^{63}

10^{63}

Compare the two: Divide a vigintillion by a trillion to see how many times larger it is.

\frac{10^{63}}{10^{12}} = 10^{51}

Interpret: A vigintillion is

10^{51}

times larger than a trillion — itself an unimaginably large factor.

Answer: A vigintillion has 63 zeros and is

10^{51}

times larger than a trillion.

Why It Matters

Names like vigintillion show how mathematicians systematically extend number naming using Latin roots. Understanding this pattern lets you decode any "-illion" name, which occasionally appears in science, national debt discussions, or combinatorics problems involving astronomically large counts.

Common Mistakes

Mistake: Confusing the short scale (US) with the long scale (older European). In the long scale, a vigintillion equals

10^{120}

, not

10^{63}

Correction: Always check which system is being used. In most modern English-speaking contexts, the short scale applies, so a vigintillion is

10^{63}