The ability of pigeons to home directly from distant, unfamiliar release sites has defied explanation because it has been impossible to identify the mechanism by which the birds determine their current position relative to their home loft. A variety of magnetic effects on homing orientation have implicated magnetic total intensity in position determination but no testable models for magnetic navigation by homing pigeons have resulted. Here, a vector summation model is proposed which identifies a novel coordinate that pigeons could use with magnetic total intensity to determine position. The model makes predictions about the accuracy of homing and patterns of homing orientation over local and regional scales. The model requires no unusual computational or cognitive abilities. It is, however, consistent with a significant volume of pigeon homing data and can be tested in a variety of ways.Copyright 1998 Academic Press Limited