angle kappa
Angle kappa is the angle between the pupillary axis and the visual axis. The pupillary axis passes through the center of the apparent pupil perpendicular to the cornea, and the visual axis connects the fixation point with the fovea.1 Of the angles between the eye's reference axes, only angle kappa can actually be measured clinically, and older literature also called angle kappa the angle lambda.1
The pupillary axis usually meets the back of the globe slightly nasal and inferior to the fovea. A fixated penlight therefore reflects from the cornea slightly nasal to the pupil center, which is a positive angle kappa.1 The average is 5° in emmetropic eyes, 7.5° in hyperopic eyes and 2° in myopic eyes. In some myopic eyes the visual axis lies temporal to the pupillary axis, which gives a negative angle kappa.2 A negative angle kappa is less common than a positive one, and a negative angle kappa is not always pathologic.1
Angle kappa can mislead the corneal reflex test. A large positive angle kappa can simulate an exodeviation or mask part of an esodeviation, and a negative angle kappa can simulate an esodeviation or mask part of an exodeviation.1
More detail
Texts define these angles against different reference lines. One glossary defines angle kappa as the angle between the optical axis and the line of sight, and angle lambda as the angle between the pupillary axis and the line of sight, which passes through the center of the entrance pupil.3 In children with cicatricial retinopathy of prematurity, the fovea can be dragged temporally, which produces a large positive angle kappa.2
Sources (7)
- von Noorden and Campos, Binocular Vision and Ocular Motility, ch. 12
- Yanoff and Duker, Ophthalmology (2023), ch. 11.3, Examination of Ocular Alignment and Eye Movements
- Pickwell's Binocular Vision Anomalies, appendix glossary
- American Academy of Ophthalmology (2020) 'Optics of the Human Eye', Basic and Clinical Science Course, Section 3: Clinical Optics.
- Basmak, H., Sahin, A., Yildirim, N., Papakostas, T.D. and Kanellopoulos, A.J. (2007) 'Measurement of angle kappa with synoptophore and Orbscan II in a normal population', Journal of Refractive Surgery, 23(5), pp. 456–460.
- Moshirfar, M., Hoggan, R.N. and Muthappan, V. (2013) 'Angle Kappa and its importance in refractive surgery', Oman Journal of Ophthalmology, 6(3), pp. 151–158.
- Rutstein, R., Daum, K. (1997) Anomalies of Binocular Vision: Diagnosis & Management, Mosby, pp. 347.
Reviewed October 2026