Quasar outflows carry mass, momentum and energy into the surrounding environment, and have long been considered a potential key factor in regulating the growth of supermassive black holes and the evolution of their host galaxies [1][2][3][4] . A crucial parameter for understanding the origin of these outflows and measuring their influence on their host galaxies is the distance (R) between the outflow gas and the galaxy center 5, 6 . While R has been measured in a number of individual galaxies 7-15 , its distribution remains unknown. Here we report the distributions of R and the kinetic luminosities of quasars outflows, using the statistical properties of broad absorption line variability in a sample of 915 quasars from the Sloan Digital Sky Surveys. The mean and standard deviation of the distribution of R are 10 1.4±0.5 parsecs. The typical outflow distance in this sample is tens of parsec, which is beyond the theoretically predicted location (0.01 ∼ 0.1 parsecs) where the accretion disc line-driven wind is launched 16,17 , but is smaller than the scales of most outflows that are derived using the excited state absorption lines 7-14 . The typical value of the mass-flow rate is of tens to a hundred solar masses per year, or several times the accretion rate. The typical kinetic-to-bolometric luminosity ratio is a few per cent, indicating that outflows are energetic enough to influence the evolution of their host galaxies.Nowadays, theoretical models for galaxy formation and evolution routinely invoke the concept of "quasar feedback"-the strong effect that the active supermassive black hole's (SMBH) energy output exerts on its host galaxy-to keep massive galaxies from forming many stars and becoming overly massive. In 10-40% of the quasars in which the central source and outflowing gas are both in the line of sight, outflows may manifest themselves as broad absorption lines (BALs) 18,19 and BAL outflows are therefore a candidate agent of quasar feedback. The importance of outflows to active galactic nucleus (AGN) feedback can be quantified using the mass-flow rate (Ṁout) and the kinetic luminosity (Ė k ) of the outflowing material. TheṀout and theĖ k of a BAL outflow can be estimated from the distance (R) between the out- * flowing gas and the galaxy center, the total hydrogen column density NH and the fraction Ω of the solid angle subtended by the outflowing gas. Because the ionization parameter UH of the plasma is inversely proportional to the product of hydrogen number density nH and R 2 , i.e., UH ∝ 1/(nHR 2 ), R can be obtained by measuring UH and nH. In general, nH can be determined from the absorption lines of the excited states of ions (e.g., Fe II*, Si II*, S IV*), but this method is hindered by line blending and is therefore only applicable to quasars with relatively narrow absorption lines. During the last decade or so, outflow distances have been measured for only about a dozen of individual quasars using this method 7-14 , while the distributions of primary properties of BAL outflows remain in unknown. ...