The potential relationship between solar activity and changes in solar diameter remains the subject of debate and requires both models and measurements with sufficient precision over long periods of time. Using the PICARD instruments, we carried out precise measurements of variations in solar diameter during the rising phase of solar cycle 24. From new correction methods we found changes in PICARD space telescope solar radius amplitudes that were less than ±20 mas (i.e. ±14.5 km) for the years 2010–2011. Moreover, PICARD ground-based telescope solar radius amplitudes are smaller than ±50 mas from 2011 to 2014. Our observations could not find any direct link between solar activity and significant fluctuations in solar radius, considering that the variations, if they exist, are included within this range of values. Further, the contribution of solar radius fluctuations is low with regard to variations in total solar irradiance. Indeed, we find a small variation of the solar radius from space measurements with a typical periodicity of 129.5 days, with ±6.5 mas variation.