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Cone-beam computed tomography (CBCT) is widely used in dental imaging, small animal imaging, radiotherapy, and non-destructive industrial inspection. The quality of CBCT images depends on the precise knowledge of the CBCT system's alignment. We introduce a distinct procedure, 'precision alignment loop (PAL)', to calibrate any CBCT system with a circular trajectory. We describe the calibration procedure by using a line-beads phantom, and how PAL determines the misalignments from a CBCT system. PAL also yields the uncertainties in the simulated calibration to give an estimate of the errors in the misalignments. From the analytical simulations, PAL can precisely obtain the source-to-rotation axis distance, and the geometric center G, 'the point in z -axis meets the detector', where the z -axis is coincident with the line from the x-ray source that intersects the axis of the rotation orthogonally. The uncertainties of three misalignment angles of the detector are within ±0.05°, which is close to ±0.04° for the results of Yang et al (2017 Med. Phys. 44 1692), but our method is easy and simple to implement. Our distinct procedure, on the other hand, yields the calibration of a micro-CT system and an example of reconstructed images, showing our calibration method for the CBCT system to be simple, precise, and accurate. [ABSTRACT FROM AUTHOR]