We prove that for Voronoi percolation on \mathbb{R}^d, there exists p_c\in[0,1] such that
- for p
c, there exists cp>0 such that \mathbb{P}_p[0\text{ connected to distance }n]\leq \exp(-c_p n),
- there exists c>0 such that for p>pc, \mathbb{P}_p[0\text{ connected to }\infty]\geq c(p-p_c).
For dimension 2, this result offers a new way of showing that pc(2)=1/2. This paper belongs to a series of papers using the theory of algorithms to prove sharpness of the phase transition.