Force accuracy as a function of the octree opening angle, Θ, in a cylindrical cosmological volume at different redshifts. We evolved 6 ⋅ 10⁴ particles in standard ΛCDM cosmology with direct force calculation in a periodic cylinder with L_z = 200.0 Mpc height and R_sim = 100.0 Mpc radius for this accuracy test. After the simulation was finished, we calculated the F_BH octree forces with our StePS simulation code. The F_D direct forces were used as a ground truth in the comparison. We calculated the octree forces with and without the radial force correction. Left: Relative total ⟨|F_BH − F_D|/|F_D|⟩ force error. The magnitude of the force error is behaving similarly as in the well tested cubic T³ case. The new radial force correction calculated from the initial particle load increases the accuracy in all redshifts. Center: Mean radial ⟨F_BH, 𝜚/F_D, 𝜚⟩ force error. While the raw radial octree force have a non-zero expected value at high Θ values, the implemented radial correction fixes this in all redshifts for Θ ≤ 0.5. It is critical to use this correction, since a systematic bias in radial direction will cause contraction or expansion of the simulated volume, which will alter the structure formation due to the changed background density. Right: Mean tangential ⟨F_BH, ϑ/F_D, ϑ⟩ force error. In contrast to the radial case, the measured tangential force errors are consistent with a zero mean. A non-zero systematic bias in this component would cause errors in the total angular momentum.