Recent advances in computer and multimedia technologies make the natural presentation of three-dimensional contents possible. Sound field reproduction techniques, such as High-Order Ambisonics (HOA), are now within the reach of commercially available computation devices. Unfortunately, content production and its coding for distribution still focuses on legacy formats, mainly stereophonic sound. This paper presents a method to extrapolate full-surround, HOA-encoded sound fields from conventional stereo mixes. The proposal assumes its input to be mixed using a conventional panning law. Its formulation resembles traditional matrix-encoded surround methods; however, it does not assume any specific layout for the loudspeakers comprising the reproduction system. The output of the proposed method is the second-order HOA encoding of a sound field in the horizontal plane spanning the full 360-degrees panorama. In this sense, the proposal outperforms traditional matrix-encoding methods by allowing sound sources to be placed freely around the listener. It also has better spatial resolution than the Ambisonics UHJ format, which is limited to first-order horizontal encodings when working with stereo signals. The proposed method is evaluated using simple stereo mixes of a wavelet panned to different positions on the horizontal plane. The extrapolated HOA-encoding exhibits stable sound-source positioning and negligible crosstalk between disjoint sources.