Using a dataset corresponding to an integrated luminosity of 3.0 fb−1 collected in pp collisions at centre-of-mass energies of 7 and 8 TeV, the B 0 → ϕϕ branching fraction is measured to be $$ \mathrm{\mathcal{B}}\left({B}_s^0\to \phi \phi \right)=\left(1.84\pm 0.05\left(\mathrm{stat}\right)\pm 0.07\left(\mathrm{syst}\right)\pm 0.11\left({f}_s/{f}_d\right)\pm 0.12\left(\mathrm{norm}\right)\right)\times 1{0}^{-5}, $$ where f s /f d represents the ratio of the B 0 to B 0 production cross-sections, and the B 0 → ϕK *(892)0 decay mode is used for normalization. This is the most precise measurement of this branching fraction to date, representing a factor five reduction in the statistical uncertainty compared with the previous best measurement. A search for the decay B 0 → ϕϕ is also made. No signal is observed, and an upper limit on the branching fraction is set as $$ \mathrm{\mathcal{B}}\left({B}^0\to \phi \phi \right)<2.8\times 1{0}^{-8} $$ at 90% confidence level. This is a factor of seven improvement compared to the previous best limit.