Galaxy clustering is a standard cosmological probe, which is commonly analysed through two-point statistics. In observations, the estimation of the two-point correlation function crucially relies on counting pairs in a random catalogue. The latter contains a large number of randomly distributed points, which accounts for the survey window function. Random pair counts can also be advantageously used for modelling the window function in the observed power spectrum. Because pair counting scales as $\mathcal{O}(N^2)$, where $N$ is the number of points, the computational time to measure random pair counts can be very expensive for large surveys. In this work we present an alternative approach for estimating those counts that does not rely on the use of a random catalogue. We derive an analytical expression for the anisotropic random-random pair counts that accounts for the galaxy radial distance distribution, survey geometry, and possible galaxy weights. Considering the cases of the VIPERS and SDSS-BOSS redshift surveys, we find that the analytical calculation is in excellent agreement with the pair counts obtained from random catalogues. The main advantage of this approach is that the main calculation only takes a few minutes on a single CPU, and does not depend on the number of random points. Furthermore, it allows an accuracy equivalent to that we would have by using a random catalogue with about 1500 times more points than in the data. We also describe and test an approximate expression for data-random pair counts that is less accurate than for random-random counts, but still provides subpercent accuracy. The presented formalism should be very useful to account for the window function in next-generation surveys, which will necessitate accurate two-point window function estimates over huge observed cosmological volumes.