pISSN: 1011-8942 eISSN: 2092-9382
Korean J Ophthalmol 2013;27(6):421-424
© 2013 The Korean Ophthalmological Society
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The Correlation between Angle Kappa and Ocular Biometry
Se Rang Choi1, Ungsoo Samuel Kim1,2
1Department of Ophthalmology, Kim’s Eye Hospital, Seoul, Korea
2Department of Ophthalmology, Konyang University College of Medicine, Daejeon, Korea
The angle kappa is defined as the angle between the vi-
sual line and the pupillary axis. In terms of refractive sur-
gery, a large angle kappa can lead to a decentered ablation,
which may produce complications, including decreased
safety and an increased likelihood of postoperative irregu-
lar astigmatism . Sensory exotropia or esotropia are per-
formed during strabismus surgery to make the eyes appear
straight, not to align the visual axes . Thus, the presence
of a large angle kappa is of great significance when plan-
ning strabismus surgery and should be considered .
Slit lamp, synoptophore or Orbscan II topography can be
used to measure the angle kappa. It can be influenced by
age, sex, refractive error, or strabismus [4,5]. However,
there is a difference of opinion on the relationship between
angle kappa and factors. Basmak et al.  reported that the
angle kappa decreased as the refractive error became more
negative. Therefore, it is smaller in myopes and larger in
hyperopes. However, Hashemi et al.  showed that the
largest angle kappa values were observed in individuals
with emmetropia. These differences might be due to ethnic
variations in ocular anatomy . A statistically larger in-
terpupillary distance, which may influence the angle kappa
, has been observed in black patients compared to white
ones. Refractive errors are also statistically different among
races. Au Eong et al.  estimated that the prevalence of
myopia in Singaporean participants (n = 110,236) was
48.5% in Chinese, 34.7% in Eurasians, 30.4% in Indians,
and 24.5% in Malays.
Received: February 6, 2013 Accepted: March 29, 2013
Corresponding Author: Ungsoo Samuel Kim, MD, PhD. Department
of Ophthalmology, Kim’s Eye Hospital, Konyang University College of
Medicine, #136 Yeongsin-ro, Yeongdeungpo-gu, Seoul 150-034, Korea.
Tel: 82-1577-2639, Fax: 82-2-2677-9214, E-mail: email@example.com
Purpose: To investigate normative angle kappa data and to examine whether correlations exist between angle kappa and oc-
ular biometric measurements (e.g., refractive error, axial length) and demographic features in Koreans.
Methods: Data from 436 eyes (213 males and 223 females) were analyzed in this study. The angle kappa was measured using
Orbscan II. We used ocular biometric measurements, including refractive spherical equivalent, interpupillary distance and
axial length, to investigate the correlations between angle kappa and ocular biometry. The IOL Master ver. 5.02 was used to
obtain axial length.
Results: The mean patient age was 57.5 ± 12.0 years in males and 59.4 ± 12.4 years in females (p = 0.11). Angle kappa aver-
aged 4.70 ± 2.70 degrees in men and 4.89 ± 2.14 degrees in women (p = 0.48). Axial length and spherical equivalent were
correlated with angle kappa (r = -0.342 and r = 0.197, respectively). The correlation between axial length and spherical equiv-
alent had a negative correlation (r = -0.540, p < 0.001).
Conclusions: Angle kappa increased with spherical equivalent and age. Thus, careful manipulation should be considered in
older and hyperopic patients when planning refractive or strabismus surgery.
Key Words: Axial length, Corneal topography, Refractive errors
Korean J Ophthalmol Vol.27, No.6, 2013
Thus, the purpose of the current study was to investigate
normative data of angle kappa using Orbscan II measure-
ments and also to estimate the correlation between angle
kappa and ocular biometrics (e.g., refractive error, axial
length) and demographic features in Koreans.
Materials and Methods
Data from 584 eyes examined between January and June
of 2011 were obtained from the Kim’s Eye Hospital data-
base, and medical records were reviewed retrospectively.
We excluded 148 eyes with a history or signs of previous
ocular trauma, anterior segment inflammation, glaucoma,
previous ocular surgery, or manifest strabismus. Data from
436 eyes (213 males and 223 females) were included in the
study’s analyses. This research study was reviewed and
approved by the institutional review board of Kim’s Eye
Hospital, and all procedures conformed to the guidelines
of the Declaration of Helsinki. Full ophthalmologic exam-
inations, including best-corrected visual acuity, slit-lamp
examination and manifest refraction, were performed.
Angle kappa was obtained with Orbscan II topography
(Bausch & Lomb/Orbtek, Rochester, NY, USA). The Orb-
scan II is a three-dimensional scanning slit topographic
device that measures the angle kappa automatically with
special software by calculating the distance between the
center of the pupil and the center of the Placido ring reflec-
tion on the cornea. The latter center represents the axis of
sight . We used the spherical equivalent, interpupillary
distance (IPD) and axial length to investigate whether cor-
relations existed between the angle kappa and ocular bio-
metric measures. IPD was measured using a millimeter
rule and common procedure . The IOL Master ver. 5.02
(Carl Zeiss, Jena, Germany) was used to measure axial
Data were analyzed using the SPSS ver. 14.0 (SPSS Inc.,
Chicago, IL, USA). Results from quantitative variables
were expressed as mean ± standard deviation, and compar-
isons between males and females were conducted using
Student t-tests. The comparison between age and angle
kappa were analyzed using one-way ANOVA. Correlations
between the angle kappa and ocular biometries were statis-
tically examined using the Pearson correlation test. Statis-
tical significance was defined as a p-value of <0.05.
The average patient age was 59.2 ± 12.6 years (57.5 ±
12.0 years in males and 59.4 ± 12.4 years in female partici-
pants, p = 0.11). Angle kappa averaged 4.70 ± 2.70 and 4.89
± 2.14 degrees in male and female patients, respectively (p
= 0.48). Normative data of the angle kappa are shown in
Fig. 1. Angle kappa was highest in male patients in 50
years of age and in female patients over 70 years of age.
After post-hoc analysis, there was a statistically significant
difference between men in their 40s and men in their 50s
(p = 0.04) and between women less than 40 years old and
women more than 70 years old (p = 0.04).
Axial length was correlated with angle kappa (r =
-0.342, p < 0.001). Similarly, the spherical equivalent was
positively correlated with angle kappa (r = 0.197, p < 0.001)
(Table 1). In addition, the correlation between axial length
and spherical equivalent had a negative correlation (r =
-0.540, p < 0.001). Angle kappa tended to be lowest in high
myopes, but there was no statistically significant difference
in angle kappa between refractive error groups (ANOVA,
p = 0.33) (Fig. 2).
This study showed that the angle kappa decreased with
axial length and increased with age and spherical equiva-
lent. The angle kappa averaged 4.70 ± 2.70 degrees in men
and 4.89 ± 2.14 degrees in women. This finding was some-
what smaller than the values observed in citizens of Teh-
ran, where it was measured as 5.41 ± 1.32 degrees in men
Fig. 1. Normative data of angle kappa and axial length (AL) ac-
cording to age.
Angle kappa (degree)
Axial length (mm)
< 3940-49 50-59
60-69 > 70
Choi SR, et al. Angle Kappa and Ocular Biometry
and 5.49 ± 1.34 degrees in women . This difference
could be due to racial differences in ocular biometric mea-
sures. Also, higher rates of myopia have been noted in Far
East Asia (including Korea) . This trend could explain
why a smaller angle kappa, which decreases with the
spherical equivalent, was observed in our study.
The angle kappa was not significantly different among
age groups, but significant differences between certain de-
cades were noted. As shown in figure 1, the angle kappa
generally increased with age in women, while the largest
angle kappa was observed in men in their 50s. The cause
of the difference is not certain. However, Fig. 1 illustrates
the slight decline of axial length in the 50s in males, and
these minimal differences might have influenced the angle
A positive correlation between angle kappa and age was
noted. Our results differed from those obtained previously
by Hashemi et al. , who found that the angle kappa de-
creased with age and that inter-gender differences were not
significant. Still, Kahn and Shaw  have reported in-
ter-gender differences in biometric measures, and the infe-
rior orbital rim significantly receded laterally in our female
population, while male subjects generally had a recession
of the entire inferior orbital rim. As a result, the eyeball
could shift laterally with age from recession of the inferior
The present results documented that the angle kappa was
correlated with the spherical equivalent positively and the
axial length negatively. Giovanni et al.  suggested that
emmetropes and hypermetropes tend to have a larger an-
gle kappa than myopes. Hashemi et al.  also presented
that angle kappa values were larger in the hypermetropic
population compared to the myopic population. Basmak et
al.  reported that normative values of angle kappa ranged
from 4.51 ± 0.11 degrees (right eye of myopic patients) to
5.73 ± 0.10 degrees (left eye of hyperopic participants), ac-
cording to the refractive status, and the authors speculated
that the corneal intercepts of the axes were located closer
to the optical axis in myopic eyes and farther away in hy-
peropic eyes. Interestingly, the present study showed a
negative correlation between angle kappa and axial length.
It is well known that spherical equivalent is highly cor-
related with axial length , and the present results also
had positive correlations. Thus, the current study suggest-
ed that myopic changes of the eyeball may induce a de-
crease of the angle kappa. Lastly, the angle kappa was not
significantly correlated with interpupillary distance, de-
spite the relatively correlation coefficient (r = -0.324, p =
In conclusion, the mean angle kappa was 4.70 ± 2.70 de-
grees in men and 4.89 ± 2.14 degrees in women. The angle
kappa increased with spherical equivalent and age. Thus,
careful manipulation should be considered both in older
patients and in hyperopic patients when planning refrac-
tive or strabismus surgery.
Conflict of Interest
No potential conflict of interest relevant to this article
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Fig. 2. Angle kappa according to refractive errors.
Hyperopia Emmetropia Myopia
Angle kappa (degree)
Table 1. Correlation between angle kappa and ocular biometries
Age 0.218 <0.001
Axial length-0.342 <0.001
Spherical equivalent 0.197<0.001
Interpupillary distance -0.324 0.163
Korean J Ophthalmol Vol.27, No.6, 2013
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