## NumberÂ ofÂ NodesÂ inÂ a Perfect BinaryÂ Tree

**How many nodes are there in a perfect binary tree?**

**2 ^{n+1} – 1.**

According to the National Institute of Standards and Technology (NIST), the number of nodes in a perfect binary tree is equivalent to 2^{n+1} – 1 (*n* stands for the tree’s height). A perfect binary tree is the one where all internal nodes have two children (degree 2), and all leaf nodes are at the same level (or depth).

This fact is verified on : October 11, 2012.