This paper presents a universal back-projection (BP) algorithm for three-dimensional photoacoustic computed tomography (PAT). The algorithm is designed for three common geometries: planar, spherical, and cylindrical. The BP formula is derived using Green's theorem and is shown to provide exact reconstructions for these geometries. A solid-angle weighting factor is introduced to account for variations in detection views. The algorithm is implemented using numerical simulations, which demonstrate its effectiveness in reconstructing the internal source distribution from measured data. The BP formula is expressed in terms of a point-spread function (PSF) and is shown to be equivalent to Fourier-domain reconstruction formulas. The algorithm is also shown to be robust to noise and can be extended to limited-angle views. The results indicate that the proposed BP algorithm is a powerful tool for PAT, offering accurate and efficient reconstruction of three-dimensional images. The algorithm is based on the principle that photoacoustic imaging is a form of diffraction tomography, and it leverages the unique properties of ultrasonic waves to reconstruct the internal structure of tissues. The algorithm is validated through numerical simulations, which demonstrate its ability to accurately reconstruct the source distribution in the presence of noise and limited-angle views. The results suggest that the BP algorithm is a promising approach for PAT, with potential applications in biomedical imaging.This paper presents a universal back-projection (BP) algorithm for three-dimensional photoacoustic computed tomography (PAT). The algorithm is designed for three common geometries: planar, spherical, and cylindrical. The BP formula is derived using Green's theorem and is shown to provide exact reconstructions for these geometries. A solid-angle weighting factor is introduced to account for variations in detection views. The algorithm is implemented using numerical simulations, which demonstrate its effectiveness in reconstructing the internal source distribution from measured data. The BP formula is expressed in terms of a point-spread function (PSF) and is shown to be equivalent to Fourier-domain reconstruction formulas. The algorithm is also shown to be robust to noise and can be extended to limited-angle views. The results indicate that the proposed BP algorithm is a powerful tool for PAT, offering accurate and efficient reconstruction of three-dimensional images. The algorithm is based on the principle that photoacoustic imaging is a form of diffraction tomography, and it leverages the unique properties of ultrasonic waves to reconstruct the internal structure of tissues. The algorithm is validated through numerical simulations, which demonstrate its ability to accurately reconstruct the source distribution in the presence of noise and limited-angle views. The results suggest that the BP algorithm is a promising approach for PAT, with potential applications in biomedical imaging.