This is a simple question, just looking for a reference for a formula.

As far I understand the genus of a prime Fano $n$-fold is defined to be the genus of a complete intersection of $n-1$ smooth divisors in the system $|-K_{X}|$ (see https://www.math.ens.fr/~debarre/ExposePoitiers2013.pdf). For $n=3$ this number equals $$\frac{(-K_{X})^3}{2} +1.$$

**Question:** What is the general formula for the genus of Fano variety?

Unfortunately I was not able to find this in the literature.