OBJECTIVE To analyze changes in the eye's refractive properties when a toric intraocular lens (IOL) rotates. METHODS Fundación Oftalmológica del Mediterráneo, Valencia, Spain. METHODS Experimental study. METHODS The matrix definition of astigmatism was used in this theoretical study and compared with another vector representation. Two methods were compared: (1) The cylinder, C, resulting from the addition of 2 cylinders C(1) and C(2) whose axes form an angle a, is obtained by the addition of 2 vectors of values C(1) and C(2) forming an angle 2a; (2) the power matrix, F, of a thin astigmatic dioptric system that decomposes naturally into 3 orthogonal components: the purely spherical part F(nes,) the ortho-astigmatism F(or), and oblique astigmatism F(ob). RESULTS The residual cylinder was one third of the corneal astigmatism when a toric IOL rotated ±10 degrees when the cylinder values for the cornea (C(1)) and IOL (C(2)) were equal. Nevertheless, in most cases C(1) is greater than C(2); therefore, the residual astigmatism did not change noticeably with small rotations. The angle of rotation, b, which annuls the astigmatism correction, could be obtained from the following: cos(π + 2b) = -r/2, with r being the ratio between the IOL and cornea cylinders. CONCLUSIONS The 2 methods gave equivalent results. When the IOL cylinder had a value different from that of the corneal astigmatism, a better choice would be a lower, rather than higher, cylinder value to reduce residual astigmatism. In general, toric IOL rotations less than 10 degrees changed the eye's refraction less than 0.50 diopter. Thus, small axis rotations are not an obstacle for satisfactory astigmatism correction with toric IOLs. BACKGROUND No author has a financial or proprietary interest in any material or method mentioned.