We present a first version of the Svalbard ice-free topography (SVIFT1.0) using a mass conserving approach for mapping glacier ice thickness. SVIFT1.0 is informed by more than one million point-measurements, totalling more than 8700 km of thickness profiles. SVIFT1.0 is publicly available and represents the geometric state around the year 2010. Our estimate for the total ice volume is 6199 km3, equivalent to 1.5 cm sea-level rise. The thickness map suggests that 13% of the glacierised area is grounded below sea-level. A complementary map of error estimates comprises uncertainties in the thickness surveys as well as in other input variables. Aggregated error estimates are used to define a likely ice-volume range of 5200 — 7300 km3. The ice-front thickness of marine-terminating glaciers is a key quantity for ice-loss attribution because it controls the potential ice discharge by iceberg calving into the ocean. We find a mean ice-front thickness of 135 m for the archipelago (likely range 123 — 158m).