We have developed simple, fast, and accurate algorithms for the linear Radon (-) transform and its inverse. The algorithms have an computational complexity in contrast to the cost of a direct implementation in 2D and an computational complexity compared to the cost of a direct implementation in 3D. The methods use Bluestein’s algorithm to evaluate discrete nonstandard Fourier sums, and they need, apart from the fast Fourier transform (FFT), only multiplication of chirp functions and their Fourier transforms. The computational cost and accuracy are thus reduced to that inherited by the FFT. Fully working algorithms can be implemented in a couple of lines of code. Moreover, we find that efficient graphics processing unit (GPU) implementations could achieve processing speeds of approximately , implying that the algorithms are I/O bound rather than compute bound.