Visual Size: Calculating a Visual Angle
A Psychology 469 (Visual Perception) Tutorial
Created by Donald Kline and Lisa Lynk
Vision and Aging Laboratory
Department of Psychology
University of Calgary
Version 1.2 – Jan. 2001
1. How to Use this Tutorial
Welcome to the PSYC 469 tutorial on Calculating a Visual Angle.
The size of an object’s image on the retinal depends on two things, the actual size
of the object, and its distance from the eye. In this tutorial, you will learn how to use
object size and object distance to calculate an image’s angular size on the retina. The
concept of an images angular size is essential to understanding a variety of visual
phenomena including acuity, depth perception, and the contrast sensitivity function (CSF)
of the visual system for objects of different size.
These tutorials cover several different topics in vision. Each topic is covered in a
separate module, which consist of repeating sequences. On the first page in each
sequence, you will receive a brief presentation of information , on the following page you
will be asked a question about that information, and on the third page, you’ll see the
question along with the correct answer to the question.
To use the tutorials, select the topic from the menu by clicking on it. Study the
information pages carefully and subsequently select the ‘next’ button. This will
automatically bring you to the question page. After recording your answer, click on
‘answer’ and the correct one will appear. If your answer is not correct, you should
review the relevant information by selecting ‘information’. This will take you to the
preceding information page. Read the page over again very carefully proceeding to the
Question and Answer once you have done so.
You can quit the tutorial anytime by returning to the main Tutorial Menu and
selecting ‘tutorial’ button located in the corner
Using The Tutorial
You should read over each information Page very carefully, and then click on
‘next’. Record your answer to the question on the question Page, and then use the
“Answer Page” link to see the correct answer. If your answer is correct, use the
Information, Question and Answer Page links to proceed onward through the tutorial.
Anytime that you answer is not correct, you should use the question Page link on the
Answer Page to return to and read the previous Information Page very carefully.
You can quit the tutorial at any time, by returning to the main Visual Perceptual Tutorial
menu. Just select the “home” button located in the lower left hand corner of every pate.
Once there, you can exit the tutorial series by selecting the quit button.
Information Page: Why Use Visual angle for Size?
In vision research, the size of objects is typically expressed in terms of its seconds
(60 seconds = 1 minute). By using this approach, objects of different real-world sizes
viewed from various viewing distances can be compared in terms of their true “visual”
size on the retinal. This approach also makes it useful for translating size discrimination
thresholds into acuity. For example, if a person can detect a minimum gap or feature that
is 1 minute across, that corresponds to a visual acuity of 20/20 regardless whether the
acuity target (e.g. a letter, grating or Landholt C) is near and smaller, or far away and
larger.
Question Page
In vision research, the retinal image size of objects of various actual sizes, viewed from
different distances can be compared using the angular unit of a.) ______________.
Using this unit, someone with 20/20 acuity is able to discriminating a target feature (e.g.,
the gap in a letter “C”) which is b.) ______________ in size, regardless of the target’s
distance from the observer.
Answer Page
Question: In vision research, the retina image size of objects of various actual sizes,
viewed from different distances can be compared using the unit of a.) ___________.
Using this unit, 20/20 acuity is equivalent to discriminating a target which is b.)
__________in size, regardless of its distance from the observer.
a.) DEGREES
b.) 1 MINUTE
Information Page
The relationship0 between the angular size of the image in otne retinal on one
hand, and target size and viewing distance on the other, can be seen below. Although
object A is twice the size of object B, it is also viewed from twice as far away (i.e. from
distance D versus 0.5D). Thus, the visual angles of object A and object B are identical on
the retina (i.e. ).
Question Page
2. As an object is moved closer to the eye its visual angle on the retina will
a.)____________. Therefore, the visual image size of an object can be specified only if
the object’s b.)___________ from the eye is also known.
Answer Page
2. As an object is moved closer to the eye its visual angle on the retinal will a.)
_________. Therefore, the visual image size of an object can be specified only if
the object’s b.)___________ from the eye is known.
a.) INCREASE
b.) DISTANCE
Information Page
If the size of an object and its distance from the eye are both known, its visual angle
(theta or  ) can be calculated using trigonometry. To use trigonometry, it is necessary to
work with right angles. For larger angles (> 6 degrees) it should be done by using the
“exact method” : 1.) multiply the object’s size (i.e. width or height) by 0.5 (i.e. 0.5A), and
divide that by the viewing distance (D) in the same units to find the tangent of the angle
0.5 : 0.5A/D = tan (0.5 ).
After finding the angle associated with the tan of 0.5 (i.e. the arc tan), all you need to do
is multiply 0.5 by 2 to get  in degrees or fractions of degrees.
Question Page
3. To calculate the visual angle () of a feature most accurately you should begin by first
calculating the a.) ____________ of 0.5 , which is equal to b.) ____________ times the
size of the feature divided by its c.) ___________.
Answer Page
3. To calculate the visual angle of () of a feature most accurately you should begin by
first calculating the a.) ____________ of 0.5 , which is equal to b.) ____________
times the size of the feature divided by its c.) ___________.
a.) TANGENT
b.) 0.5
c.) DISTANCE
Information Page
Here’s an example of how the angular size of a 7cm x 7cm, square 6 meters away from
the observer’s eye would be calculated.
Tan (0.5) = (0.5 x 7cm)/(6 x 100cm)
= 3.5/600
= 0.0058
0.5 = tan –1 (0.0058)
= 0.3323 degrees
 = 2 x 0.3323
= 0.665 degrees ( or 0.665 x 60 ) = 39.9 minutes
Question Page
4. Calculate the visual angle size of an 8cm feature at a 100-cm viewing distance
using the “exact” method. The tan of 0.5 is equal to a.) _____________ , which
corresponds to an angle of b.) ___________ degrees. The visual angle of the feature
is therefore c.) ____________ degrees or d.) ___________ degrees and e.) ________
minutes.
Answer Page
4.)
a.) 0.04
b.) 2.29
c.) 4.58
d.) 4
e.) 34.8
Information Page
Small Angle Approximation Method: for smaller objects or features (less than 6
degrees or so), the visual angle can be approximated closely and quickly without first
finding 0.5. Instead, all you do is divide feature size by viewing distance to find tan
, and thus  itself.
tan  = (size of object in cm)/(distance in dm)
 = arctan (size)/(distance)
Question Page
5. Using the “small andgle” approximation method, calculate the visual angle of a
48 cm target feature that is viewed from 6 meters. The tangent of this visual angle is
a.) _____________ and the visual angle is b.) ______________ degrees.
Answer Page
5.
a.) 0.08
b.) 4.58
Information Page
Compare your answers to question 4 and 5 on the preceding cards. You will see that
although you used the “exact” method on question 4, and the “small angle
approximation” method on number 5, the visual angle size was virtually the same
(about 4.58 degrees) in both cases. Because the angular size of the two targets was
small (less that 6 degrees), it didn’t matter if the angle was calculated from tan  or
from tan 0.5.
A Useful “ Rule of Thumb”
To provide a quick check of the general accuracy of your visual angle calculation,
you can use the “thumb test”. The width of your thumb held at arms length is
approximately 2 degrees of arc. If you simply compare the width of your thumb at
arms length to an object or feature, you can make a quick approximation of its visual
angle at your eye. For example, if a stimulus is about one-half the width of your
themb when viewed from the proper viewing distance, and if your calculation shows
that it is about 1.0 degree wide, it is probably correct.
Question Page
6. If you place yourself at the correct viewing distance from an obje t that your
calculations have indicated is 60 minutes wide, when you view the object against
your thumb at arm’s length it should be approximately a.) ___________ the width of
your thumb.
Answer Page
a.) half