Traffic congestion has been a pervasive problem in many urban areas of this country. This paper studies the potential of carpooling among unrelated partners (i.e., inter-household carpooling) for demand reduction during peak commute hours. Basic questions about this potential include the following. Can the current population density, origin-destination distribution, tolerable pick-up and drop-off delays, departure time distribution, and the tolerance for deviation from preferred departure time support a sizable carpooling population that can make a significant contribution to traffic demand reduction? Could the proportion of long trips that are likely candidates for carpooling (e.g., those long trips with same O-D) be so small that no significant traffic demand reduction could be expected from carpooling? The potential depends on many factors, some of which are more amenable to quantification than others. Our approach to assessing the potential is to separate such quantifiable factors from the rest, and then, based on these quantifiable factors, identify likely upper bounds for the potential. This paper focuses on a simplified urban sprawl in which the densities of workers and jobs are uniform over an infinitely large flat geographical area. For our numerical study, we use the job and worker data of the city of Los Angeles to approximate the worker/job density. An entropy optimization model that is equivalent to the gravity model is used for trip distribution. Under the assumptions made in the paper, carpooling among unrelated partners has little potential for demand reduction. Key Words: Carpool, Demand Management, Urban Sprawl, Trip Distribution, Entropy Optimization