Interplanetary magnetic clouds, although not dominant, are a relatively common feature of the solar wind at 1 AU. Their diameters at 1 AU fall in the range of 0.2--0.4 AU, and they have enhanced field strength (B≂15--30 nT at 1 AU), and lower plasma temperature and density than the surrounding plasma. The internal field is a magnetic force-free configuration, and therefore the current density (J ) is proportional to B everywhere: J=&agr;B, giving ∇¿B=&agr;B. If &agr; is constant throughout the cloud (Burlaga, 1988), then ∇2B=-&agr;2B, which has a cylindrically symmetric field solution that is consistent with observations: the axial field is proportional to the zeroth-order Bessel function of r, where r is the perpendicular distance from the cloud's axis, the tangential component is proportional to the first-order Bessel function, and the radial component is zero. We have developed a least squares program that fits magnetic field data within a cloud to these functions and which estimates various properties of the cloud, such as its size, maximum B, and inclination of its axis, as well as closest approach distance of the spacecraft. Results of a study of 18 clouds observed at 1 AU indicate that the most probable direction of the cloud's axis is within 15¿ of the ecliptic plane and ≂100¿ from the Sun's direction when it is projected into the ecliptic plane. A broad range of orientations is observed with some extending to 80¿ from the ecliptic. Other statistical properties are presented, and three cases are discussed in detail. ¿ American Geophysical Union 1990