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A wide variety of interfaces occurring in nature need to be described by their roughness, i.e. by the fluctuations of the interface's position. Although many alternative definitions exist for the roughness, they all present self-affinity as a result of scale invariance. In other words, the roughness evolves with a characteristic length scale L as A*L^ζ, with A the roughness amplitude and ζ the roughness exponent. The relevance of the roughness exponent relies on that it permits the classification of the interfaces in different universality classes. In particular, for magnetic domain walls the roughness exponent can be directly related to the different static and dynamics regimes, and hence the importance of measuring it.In this work, we study the roughness of domain walls in magnetic thin films with perpendicular anisotropy under the effect of out-of-plane and in-plane magnetic fields. Experimentally, we achieve this by means of polar magneto-optical Kerr effect (PMOKE) microscopy. We also analyze numerically the geometry of the domain walls generated by a simple scalar-field model, which has already been used to simulate quasi-bidimensional systems with perpendicular anisotropy and quenched disorder. We discuss the importance of making a statistical evaluation of both the roughness exponent ζ and roughness amplitude A, and show that our intuitive understanding of roughness is enclosed in the amplitude rather than the exponent. What is the corresponding universality class for the obtained values of the roughness exponent is a question that remains open.