Online Area of a Circle Calculator
HOW TO USE THE AREA OF A CIRCLE CALCULATOR
We can use the calculator to check the area of a circle by following these steps:
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If you enter radius as the input, then the diameter and area will be calculated.
If you enter diameter as the input, then the radius and area will be calculated.
If you enter the area as the input, then the radius and diameter will be calculated.
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Click on the ‘Example’ button to play with random input values.
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If you want to calculate something when you are in the ‘Explore’ section, all you need to do is click on the ‘Calculate’ button.
What is a Circle?
A circle is a closed two-dimensional shape in which each point on its boundary is equidistant from a point called the ‘center’.
What are the different terms related to a circle ?
There are a few simple terms that are related to every circle. We will look at the definition of three important terms, the radius, the diameter and the circumference for any given circle.
Radius
The radius of a circle is a line that is drawn from the center to the boundary of the circle. In the image shown here, the radius is represented by ‘r’.
Diameter
The diameter of a circle is a line that passes from one point on the boundary, through the center, and meets the boundary on the opposite side. The diameter also divides the circle into two equal parts. Represented by ‘d’ in the image, we can also observe that the diameter is equal to two times the radius.
Hence, d = 2r.
Circumference of a Circle
If we cut a circle and lay it out as a straight line, then the length of this line is called the circumference of the circle. We can observe that the circumference is the length of the boundary of the circle and is usually represented by the letter ‘C’.
The general formula to calculate the circumference of a given circle with radius ‘r’ is written as,
Circumference of a circle, C = 2πr
Area of a circle
The area of the circle is the measure of the space or the region enclosed inside the boundary of the circle.
There are two methods for calculating the area of a circle. It could be based on measurement of radius, or diameter.
1. Area of a circle using the radius
If we know the radius of a circle, then the formula to calculate the area is:
Area of a circle, \(A={\pi}r^2\)
We also need to note that the value of pi (π) is either \(\frac{22}{7}\) or 3.14, and r is the radius of the circle.
2. Area of a circle by using the diameter
If we know the diameter of a circle, we can calculate the the area using,
Area of a circle, \(A=\frac{{\pi}d^2}{4}\)
This is because, \(r=\frac{d}{2}\), or the radius “r” is half of the diameter, “d”.
Solved Examples on Area of a Circle Calculator
Example 1: Find the area of a circle with a radius of 3 centimeters.
Solution:
Given, r = 3 cm
The area of a circle is \({\pi}r^2\).
\({\Rightarrow}A={\pi}{\times}3^2\)
\({\Rightarrow}A=9{\pi}\) (Substituting the value of pi)
\({\Rightarrow}A={\text{28.27cm}^2}\)
Example 2: Find the diameter of a circle with an area of 154 square units.
Solution:
The area of the circle is 154 square units.
The area of circle formula is \({\pi}r^2\)
\({\Rightarrow}154 ={\pi}r^2\)
\({\Rightarrow}154=\frac{22}{7}r^2\)
\({\Rightarrow}r^2=\frac{154\times7}{22}\)
\({\Rightarrow}r^2=49\)
\({\Rightarrow}r=\sqrt{49}\)
\({\therefore} r=7\)
Since, d = 2r
\({\Rightarrow}d=2{\times}7\) = 14 units
Pi or “π” , is an irrational number and its value is taken to be “3.14” in its decimal form. When this same value is written as a fraction, the value of π is taken to be \(“\frac{22}{7}”\).
We know that the diameter of a circle is always equal to twice the length of the radius “r” of the same circle. So this is represented as d = 2r, where “d” is the diameter.
Hence the circumference of a circle, C = 2πr = πd
Where, d = the diameter of a circle
- Mark a point on a sheet of paper and name it as the center “O”.
- Place the pointer of the compass on the zero mark of a ruler and by extending the compass to the suitable mark on the ruler you get the radius.
- Place the tip of the compass at centre O.
- And by maintaining the radius that you just measured, draw the circle around the center O.
In all cases when a single diameter is drawn in a circle it divides the circle into two equal parts. Each of these parts is known as a “semi-circle.”