The finite degree formula for normalized volumes

Let $f\text{\hspace{0.17em}⁣}:(x\in (X,{\mathrm{\Delta }}_X))\to (y\in (Y,{\mathrm{\Delta }}_Y))$ be a finite surjective morphism between klt singularities such that $K_X+{\mathrm{\Delta }}_X=f^{\ast }(K_Y+{\mathrm{\Delta }}_Y)$. We show that the normalized volumes satisfy $$\widehat{\mathrm{v}\mathrm{o}\mathrm{l}}(x,X,{\mathrm{\Delta }}_X)=\mathrm{d}\mathrm{e}\mathrm{g}(f)\cdot \widehat{\mathrm{v}\mathrm{o}\mathrm{l}}(y,Y,{\mathrm{\Delta }}_Y)\mathrm{.}$$ This proves a conjecture in [LLX20, Zhu25, XZ26a].