The mass and radius are two fundamental properties to characterize exoplanets but only for a relatively small fraction of exoplanets are they both available. The mass is often derived from radial velocity measurements while the radius is almost always measured with the transit method. For a large number of exoplanets, either the radius or the mass is unknown, while the host star has been characterized. Several mass-radius relations dependent on the planet's type have been published which often allow to predict the radius, as well as a bayesian code which forecasts the radius of an exoplanet given the mass or vice versa. Our goal is to derive the radius of exoplanets using only observables extracted from spectra used primarily to determine radial velocities and spectral parameters. Our objective is to obtain a mass-radius relation that is independent of the planet's type. We work with a database of confirmed exoplanets with known radii and masses as well as the planets from our Solar System. Using random forests, a machine learning algorithm, we compute the radius of exoplanets and compare the results to the published radii. Our code, BEM, is available online. On top of this, we also explore how the radius estimates compare to previously published mass-radius relations. The estimated radii reproduces the spread in radius found for high mass planets better than previous mass-radius relations. The average error on the radius is 1.8R_Earth_ across the whole range of radii from 1 to 22R_Earth_. We found that a random forest algorithm is able to derive reliable radii especially for planets between 4 and 20R_Earth_, for which the error is smaller than 25%. The algorithm has a low bias but still a high variance, which could be reduced by limiting the growth of the forest or adding more data. The random forest algorithm is a promising method to derive exoplanet properties. We show that the exoplanet's mass and equilibrium temperature are the relevant properties which constrain the radius, and do it with higher accuracy than the previous methods.