The tool, called a Smart Reamer is used to perform the widening, in real-time of a well, in particular an oil or natural gas well, while measuring probes connected to said tool simultaneously record data relating to the geometry of the drilling operation (well diameter, diameter of the widened zone, relative position of the cutting, widening and stabilizing blocks) and data relating to the properties of the drilling fluid, with the aim of monitoring the well-widening operation without stopping drilling or extracting the drill pipes.