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Beam hardening artefacts deteriorate the reconstructed image quality in industrial computed tomography. The appearances of beam hardening artefacts can be cupping effects or streaks. They impair the image fidelity to the object being scanned. This work aims at comparing a variety of commonly used beam hardening correction algorithms in the context of industrial computed tomography metrology. We choose four beam hardening correction algorithms of different types for the comparison. They are a single‐material linearization algorithm, a multimaterial linearization algorithm, a dual‐energy algorithm and an iterative reconstruction algorithm. Each beam hardening correction algorithm is applied to simulated data sets of a dual‐material phantom consisting of multiple rods. The comparison is performed on data sets simulated both under ideal conditions and with the addition of quantum noise. The performance of each algorithm is assessed with respect to its effect on the final image quality (contrast‐to‐noise ratio, spatial resolution), artefact reduction (streaks, cupping effects) and dimensional measurement deviations. The metrics have been carefully designed in order to achieve a robust and quantifiable assessment. The results suggest that the single‐material linearization algorithm can reduce beam hardening artefacts in the vicinity of one material. The multimaterial linearization algorithm can further reduce beam hardening artefacts induced by the other material and improve the dimensional measurement accuracy. The dual‐energy method can eliminate beam hardening artefacts, and improve the low contrast visibility and dimensional measurement accuracy. The iterative algorithm is able to eliminate beam hardening streaks. However, it induces aliasing patterns around the object edge, and its performance depends critically upon computational power. The contrast‐to‐noise ratio and spatial resolution are declined by noise. Noise also increases the difficulty of image segmentation and quantitative analysis.