The mass of extraterrestrial material accreted by the Earth as submillimeter particles has not previously been measured with a single direct and precise technique that samples the particle sizes representing most of that mass. The flux of meteoroids in the mass range 10(-9) to 10(-4) grams has now been determined from an examination of hypervelocity impact craters on the space-facing end of the Long Duration Exposure Facility satellite. The meteoroid mass distribution peaks near 1.5 x 10(-5) grams (200 micrometers in diameter), and the small particle mass accretion rate is (40 +/- 20) x 106 kilograms per year, higher than previous estimates but in good agreement with total terrestrial mass accretion rates found by geochemical methods. This mass input is comparable with or greater than the average contribution from extraterrestrial bodies in the 1-centimeter to 10-kilometer size range.