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Circle Graph Formula
Circle graphs also known as pie charts are one of the most commonly used graphs to represent data using the attributes of circles, spheres, and angular data to represent realworld information. It is used to visualize information and data. In a circle graph, the whole circle which subtends a 360degree angle at the center is broken into different parts with angles of different measures. Each of these smaller parts is called arcs and these arcs are named according to their angles. Let's look into the below representation of a circle graph and understand the circle graph formula in detail.
What is Circle Graph Formula?
Whenever some data has to be represented visually as a fractional part of a whole, we use circle graphs. Circle graphs or pie charts are used to display the percentage of the total. It is used to perfectly compare the areas and see why one is smaller/greater than the other.
Therefore, when we are dealing with a limited number of buckets and discrete data sets, it’s better to use a pie chart.
Let's look into the below circle graph formulas.
Percentage of a Category = (Amount in the Category / Total) × 100
The angle subtended by the category = (Amount in the Category ⁄ Total) × 360°
Let's look into some solved examples on the circle graph formula.
Solved Examples of Circle Graph Formula

Example 1: The following circle graph shows the activities of Diana in a week.
a) Calculate the central angle subtended at sleeping.
b) Find the portion spent at school.
c) Calculate the time spent on TV per day.
d) Find the portion spent playing or sleeping.
Solution:
Using the circle graph formula the below can be calculated.
a) Time spent on sleeping \[\begin{align} &= \dfrac{34}{100}\\&= \dfrac{34}{100} \times 360\\ &=122.4 ^\circ\end{align}\]
Therefore, the central angle at sleeping = 12.4^{o}
b) Time at school \[\begin{align}&= \dfrac{25}{100}\\&=\dfrac{1}{4}\end{align}\]
Therefore, portion spent at school = 1/4
c) Time spent on TV per day \[\begin{align}&= \dfrac{8}{100} \times 24\\ &=1.92\text{ hours}\\ &= 1\text{ hour} 55\text{ minutes}\end{align}\]
Thus, time spent on TV per day = 1 hour 55 minutes
d) Portion spent on playing or sleeping\[\begin{align}&=\dfrac{8}{100} + \dfrac{34}{100}\\&=\dfrac{42}{100}\\&=\dfrac{21}{50}\end{align}\]
Thus, portion spent on playing or sleeping= 21/50

Example 2: The circle graph shows the favorite subjects of students in a class. Using the information given in the pie chart, determine the percentage of students who chose English using the circle graph formula.
Solution:
We know that \(144^\circ +36^\circ+72^\circ+108^\circ= 360^\circ\)
Using circle graph formula,
The percentage of students who chose English \[\begin{align}&=\dfrac{72}{360}\times 100\\&=20\end{align}\]
Thus, the percentage of students who chose English = 20
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