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We use the isometric embedding of the spatial horizon of fast rotating Kerrblack hole in a hyperbolic space to compute the quasi-local mass of the horizonfor any value of the spin parameter $j=J/m^2$. The mass is monotonicallydecreasing from twice the ADM mass at $j=0$ to $1.76569m$ at $j=\sqrt{3}/2$. Itthen monotonicaly increases to a maximum around $j=0.99907$, and finallydecreases to $2.01966m$ for $j=1$ which corresponds to the extreme Kerr blackhole.

The Kijowski--Liu--Yau quasi-local mass of the Kerr black hole horizon