The maximum number of bitcoins that will ever be in circulation is 21 million. Since each bitcoin can be divided into 100 million pieces — referred to as satoshis — the maximum number of bitcoin pieces that will ever be in circulation is 2100 trillion. Two reasons this choice was a great idea involve floating point arithmetic and the global money supply.

 

Floating Point Arithmetic

Floating point arithmetic is a type of mathematics used by computers to handle decimals. Decimals are often represented with 64 bits. In that case, one bit denotes the sign, 11 bits denote an exponent, and, 52 bits denote a fraction. To avoid rounding errors, it is a good idea to avoid integers that cannot be represented with just the fraction bits. To be extra safe, it may help to furthermore only use 51 of the 52 fraction bits. The maximum integer that can represented with 51 bits is slightly over 2100 trillion or the maximum possible number of bitcoin pieces.

Global Money Supply

One wise choice for a cryptocurrency is to be able to replace all the money in the world. There are many ways to estimate the global money supply. One estimate that includes the most liquid assets is referred to as M1. Around the time bitcoin was designed, the global M1 money supply was approximately $21 trillion. In the most extreme case, this $21 trillion would be spread amongst different accounts each containing a single cent. This maximum number of accounts is therefore 2100 trillion or the maximum possible number of bitcoin pieces.

 

Conclusion

Although the maximum number of bitcoins and satoshis seems arbitrary, there are sound reasons for the selected choice. It is compatible with most common computer systems, and, it is likely to be able to replace all the money used all over the world should that ever be necessary.