How many nodes are there in a perfect binary tree?

2ⁿ⁺¹ – 1.

According to the National Institute of Standards and Technology (NIST), the number of nodes in a perfect binary tree is equivalent to 2ⁿ⁺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).