We present a method for calculating the nucleon form factors of $G$-parity-even operators. This method combines chiral effective field theory ($\chi$EFT) and dispersion theory. Through unitarity we factorize the imaginary part of the form factors into a perturbative part, calculable with $\chi$EFT, and a non-perturbative part, obtained through other methods. We consider the scalar and electromagnetic (EM) form factors of the nucleon. The results show an important improvement compared to standard chiral calculations, and can be used in analysis of the low-energy properties of the nucleon.