Over the last years, radio detection has matured to become a competitive method for the detection of air showers. Arrays of thousands of antennas are now envisioned for the detection of cosmic rays of ultra high energy or neutrinos of astrophysical origin. The data exploitation of such detectors requires to run massive air-shower simulations to evaluate the radio signal at each antenna position. In order to reduce the associated computational cost, we have developed a semi-analytical method for the computation of the emitted radio signal called Radio Morphing. The method consists in computing the radio signal of any air-shower at any location from the simulation of one single reference shower at given positions by i) a scaling of the electric-field amplitude of this reference shower, ii) an isometry on the simulated positions and iii) an interpolation of the radio pulse at the desired position. This technique enables one to compute electric field time traces with characteristics very similar to those obtained with standard computation methods, but with computation times reduced by several orders of magnitude. In this paper, we present this novel tool, explain its methodology, and discuss its application extents.