Knowledge of the Solar Diameter Imager and Surface Mapper (SODISM) plate scale is a fundamental parameter for obtaining the solar radius. We have determined the plate scale of the telescope on the ground and in flight onboard the Picard spacecraft. The results show significant differences; the main reason is that the conditions of observation are not the same. In addition, the space environment has an impact on the performance of a metrology instrument. Therefore, calibration in space and under the same conditions of observation is crucial. The transit of Venus allowed us to determine the plate scale of the SODISM telescope and hence the absolute value of the solar radius. The transit was observed from space by the Picard spacecraft on 5 - 6 June 2012. We exploited the data recorded by SODISM to determine the plate scale of the instrument, which depends on the characteristics of optical elements (mirrors, filters, or front window). The mean plate scale at 607.1 nm is found to be 1.0643 arcseconds pixel−1 with 3×10−4 RMS. The solar radius at 607.1 nm from 1 AU is found to be equal to 959.86 arcseconds.