How important is an independent diameter measurement for the determination of stellar parameters of solar-type stars? When coupled with seismic observables, how well can we determine the stellar mass? If we can determine the radius of the star to between 1% and 4%, how does this affect the theoretical uncertainties? Interferometry can provide an independent radius determination, and it has been suggested that we should expect at least a 4% precision on such a measurement for nearby solar-type stars. This study aims to provide both qualitative and quantitative answers to these questions for a star, such as our Sun, where seismic information will be available. We show that the importance of an independent radius measurement depends on the combination of observables available and the size of the measurement errors. It is important for determining all stellar parameters and in particular the mass, where a good radius measurement can even allow us to determine the mass with a precision better than 2%. Our results also show that measuring the small frequency separation δν significantly improves the determination of the evolutionary stage τ and the mixing-length parameter α.