Using administrative data from England, we estimate the effect of home broadband speed on student-level value-added test scores. Our primary estimation leverages jumps in connection quality between close neighbors across thousands of invisible telephone exchange station catchment area boundaries. We find that home broadband speed has positive effects on general measures of human capital, with these effects concentrated among high-ability students and those not eligible for free school meals. These positive outcomes result from more education-oriented internet use. However, these effects are observed only for students who attend schools with faster broadband connections. Our study documents a complementarity between home and school technology in relation to general measures of human capital. Policies introducing new learning technologies should take this complementarity into account.