In the early 1990s , contemporary interstellar dust penetrating deep into the heliosphere was identified with the in-situ dust detector on board the Ulysses spacecraft . Between 1992 and the end of 2007 Ulysses monitored the interstellar dust stream . The interstellar grains act as tracers of the physical conditions in the local interstellar medium surrounding our solar system . Earlier analyses of the Ulysses interstellar dust data measured between 1992 and 1998 implied the existence of a population of ’ big ’ interstellar grains ( up to \mathrm { 10 ^ { -13 } kg } ; ) . The derived gas-to-dust-mass ratio was smaller than the one derived from astronomical observations , implying a concentration of interstellar dust in the very local interstellar medium ( ) . In this paper we analyse the entire data set from 16 years of Ulysses interstellar dust measurements in interplanetary space . This paper concentrates on the overall mass distribution of interstellar dust . An accompanying paper ( ) investigates time-variable phenomena in the Ulysses interstellar dust data , and in a third paper we present the results from dynamical modelling of the interstellar dust flow applied to Ulysses ( ) . We use the latest values for the interstellar hydrogen and helium densities , the interstellar helium flow speed of \mathrm { v _ { ISM \infty } = 23.2 km s ^ { -1 } } , and the ratio of radiation pressure to gravity , \beta , calculated for astronomical silicates . We find a gas-to-dust-mass ratio in the local interstellar cloud of R _ { g / d } = 193 ^ { +85 } _ { -57 } , and a dust density of ( 2.1 \pm 0.6 ) \times 10 ^ { -24 } \mathrm { kg m ^ { -3 } } . For a higher inflow speed of \mathrm { 26 km s ^ { -1 } } , the gas-to-dust-mass ratio is 20 % higher , and , accordingly , the dust density is lower by the same amount . The gas-to-dust mass ratio derived from our new analysis is compatible with the value most recently determined from astronomical observations ( ) . We confirm earlier results that the very local interstellar medium contains ’ big ’ ( i.e . \mathrm { \approx 1 \mu m } -sized ) interstellar grains . We find a dust density in the local interstellar medium that is a factor of three lower than values implied by earlier analyses .