Let's assume that the B-tree has, on average, a entries in each node, and b child nodes per node:

In that case, the number of entries in the tree follows a finite geometric series with a ratio of b and the first term equalling a:

N = a + ab + ab² + ab³ + ... + abⁿ

= a(1-bⁿ⁺¹)/(1-b)

N(1-b)/a = 1-bⁿ⁺¹

bⁿ⁺¹ = 1 - N(1-b)/a

n = log_b(1 - N(1-b)/a) - 1

Source: https://www.geeksforgeeks.org/dsa/b-tree-in-python/