ABSTRACT One of the main science motivations for the ESA PLAnetary Transit and Oscillations (PLATO) mission is to measure exoplanet transit radii with 3 per cent precision. In addition to flares and starspots, stellar oscillations and granulation will enforce fundamental noise floors for transiting exoplanet radius measurements. We simulate light curves of Earth-sized exoplanets transiting continuum intensity images of the Sun taken by the Helioseismic and Magnetic Imager (HMI) instrument aboard the Solar Dynamics Observatory (SDO) to investigate the uncertainties introduced on the exoplanet radius measurements by stellar granulation and oscillations. After modelling the solar variability with a Gaussian process, we find that the amplitude of solar oscillations and granulation is of order 100 ppm – similar to the depth of an Earth transit – and introduces a fractional uncertainty on the depth of transit of 0.73 per cent assuming four transits are observed over the mission duration. However, when we translate the depth measurement into a radius measurement of the planet, we find a much larger radius uncertainty of 3.6 per cent. This is due to a degeneracy between the transit radius ratio, the limb darkening, and the impact parameter caused by the inability to constrain the transit impact parameter in the presence of stellar variability. We find that surface brightness inhomogeneity due to photospheric granulation contributes a lower limit of only 2 ppm to the photometry in-transit. The radius uncertainty due to granulation and oscillations, combined with the degeneracy with the transit impact parameter, accounts for a significant fraction of the error budget of the PLATO mission, before detector or observational noise is introduced to the light curve. If it is possible to constrain the impact parameter or to obtain follow-up observations at longer wavelengths where limb darkening is less significant, this may enable higher precision radius measurements.