The form factors of the nucleon are quantities widely used in the forefront of nuclear physics research. Its calculation from first principles is still an open problem that limits our knowledge of the nucleon. In this talk I will show how, using constrains from unitarity, one can find a representation for the spectral functions that allow us to compute much more efficiently the nucleon form factors with chiral effective field theory. This new approach, that we called Dispersively Improved Chiral Effective Field Theory, overcomes the known limitations of previous chiral calculations, and becomes competitive with other ab initio determinations of the nucleon form factors. As a practical application, I will show how this approach allows us to extract reliably the proton radius from current data without the need of any extrapolation to Q^2 = 0.