Sizewise Big Number Explainer

What it is for

Big numbers turn up in news, science and games: 8 billion people, 2^64 grains of rice, 52! ways to shuffle a deck. The Big Number Explainer takes such a number and tells you its digits, its scientific notation and its names, then makes it tangible with a counting time and a stack of banknotes, and places it among famous numbers.

It also clears up a common confusion: in English a billion is 10^9, while in German, French, Spanish and most of continental Europe a Billion (or billion) is 10^12. The tool gives both the short scale and the long scale name.

Worked example

Enter 2^64 with a counting speed of 1 per second. The summary reads: 2^64 = 1.84467 × 10^19 (about 18.4 quintillion), 20 digits. The long-scale name is about 18.4 trillion, and the full digits are 18 446 744 073 709 551 616.

To make it feel real says: counting to it at one per second takes 585,000,000,000 years, 42.4 times the age of the universe. A stack of that many US banknotes would be 0.213 light years high.

The famous numbers nearby include the grains of rice on a chessboard (2^64 − 1, "about the same"), the seconds since the Big Bang (your number is 42.4 times as large) and the positions of a Rubik's Cube (43 252 003 274 489 856 000; your number is 1/2.34 as large).

For a googol the tool answers ten duotrigintillion in the short scale and ten sexdecilliard in the long scale, with 101 digits.

How to read the result

• Scientific notation rounds to six significant digits; All digits shows the exact value when it is known.
• Digits counts the digits of the integer part.
• Short scale (US, UK) and Long scale (continental Europe) use the Conway–Wechsler naming system. "About" means the number was rounded to three significant digits for the name.
• To make it feel real uses the Julian year and the age of the universe from Planck 2018 (13.787 billion years). The banknote stack uses 0.0043 in per US note.
• Nearest famous numbers each come with a source line, for example the SI definition or the person who named it.

Tips and common mistakes

• Inputs can be digits with separators (8,117,059,282), words (1.5 trillion), scientific notation (6.02e23, 3 × 10^8), powers (2^64), factorials (52!) and googol or googolplex.
• Numbers are exact up to 20,000 digits. Beyond that only the size is kept, and the result says so.
• A googolplex has more digits than there are atoms in the observable universe, so it is shown as 10^(1 × 10^100) without digits or names.
• Change the counting speed to match the question, for example 1,000 per second for a computer.
• The names are English. Other languages often use the long scale, so translate with care.

FAQ

Is a billion 10^9 or 10^12?

In today's English (short scale) 10^9. In the long scale used in much of continental Europe, 10^9 is a milliard and 10^12 a billion.

Where do the names beyond decillion come from?

From the Conway–Wechsler system, which builds Latin-based names for any power of a thousand.

Why is a very large number not exact?

Above 20,000 digits keeping every digit would be slow and useless; the tool keeps the logarithm instead.

Can I use it in the app?

Yes, the Big numbers view in Sizewise shows the same results with a ruler of powers of ten.