Acoustic absorption of materials typically depends on the characteristics of the incident sound field. Differences in the incident sound field between one laboratory and another, or between the laboratory and in situ, may therefore lead to differences in the measured absorption for the same material. To overcome this problem, a new method is proposed to measure acoustical absorption using a spherical microphone array. With this method one measures simultaneously the acoustic absorption as well as the incident sound field. The incident sound field and the reflected sound field are separated by the spherical microphone array using spatial filtering, or beamforming. The acoustic absorption is then determined from the amplitudes of the incident and the reflected fields. The measurement method may also be useful for verifying sound field diffusivity in a reverberation chamber when measuring diffuse-field absorption. Furthermore, absorption coefficients measured under in-situ sound fields may yield more accurate computer-based sound field simulations than diffuse-field absorption coefficients when the in-situ sound field is not diffuse.