We present a method to generate quantitative cross-sectional maps of acoustic propagation speed in tissue using the photoacoustic principle. The method is based on the interaction of laser-induced ultrasound from an extraneous absorber with the object under photoacoustic investigation. The propagation times of the ultrasound transients through the object at angles around 360° are measured using a multielement ultrasound detector. The geometry lends itself to fan-beam reconstruction allowing speed-of-sound tomograms to be generated. Simultaneously, conventional photoacoustic computed tomography can be performed as well. We demonstrate the concept showing results on phantoms carrying speed-of-sound distributions.