Calculate the day number of the year
JavaScript ES6, 81 69 bytes

(y,m,d)=&gt;d+parseInt("03479cehkmpr"[--m],36)+m*28-(y%(y%25?4:16)&amp;&amp;m&gt;1)


Assuming months are 1-based, otherwise I could save 2 bytes.

Edit: Saved 12 bytes using @user81655's tip.