Do you want to know how to calculate the area of a circle? Here we explain it to you quickly and easily to find the value of the area of a given circle.
This is a problem that frequently occurs in mathematics classes, specifically in geometry, and it consists of calculating the area of a circle.
What do you need to calculate the area of a circle?
- Basic formula: Area = Π xr 2
- Pi value (Π): 3.1415
- Circle data: radius, diameter or circumference.
- Calculator.
Now let’s see how to find the area of a circle.
How to calculate the area of a circle?
The circle is formed by a circumference, a closed contour and a space inside called area. In order to know how to calculate the area of a circle, you must first know the basic formula to obtain the area of a circle , and it is:
Area = Π xr 2
It’s not a complicated formula, you just need the Pi value ( Π ) and the radius of the circle ( r ).
To calculate the area of a circle we can use the radius, also the diameter, but we will always need to use the number Pi, which is written and has a periodic value of 3.14.
Radius: This is the distance between the center of the circle and the outline.
Diameter: is the width of the circle, which is measured starting from a specific point on the circumference, and ending on the opposite side through the center of the circle.
The formulas that can be used to calculate the area of a circle are:
- Calculate the area with the radius: Area = Π xr 2
- Calculate the area with the diameter: Area = (Π/4) x D 2
To calculate the surface area of a circle, use the formulas where r is the radius and D is the diameter of the circle.
We can also do it with the formula that is used to find the area of regular polygons:
Area = perimeter x apothem/2 = (2 x Π xr)/2 = 2 x Π xr 2 /2 = Π xr 2
Calculating the area of a circle using the radius
The radius is the distance from the center of the circle to any point on the edge of the circumference. The radius is half the diameter, and then we’ll see how to calculate the area when you have the diameter instead of the radius.
The formula is simple:
Area = Π xr 2
Let’s do an example to see how simple it is. Suppose a circle with a radius of 3 centimeters.
The variable r that represents the radius, in this case is equivalent to 3 cm, and must be raised to the square:
A = Π x 3 2 = Π x 9
Now all that remains is to multiply this value by Pi, the mathematical constant that represents the ratio between the area of the circle and the radius, and it is worth 3.14.
A = Π x 9 = 3.14 x 9 = 28.26 centimeters2.
Do not forget that the area must be expressed in units squared . If the area is measured in centimeters, the result of the area will be in square centimeters. In the case of the example, it is 28.26 cm2.
Another way of expressing the result could be 9Π cm2.
Calculate the area of a circle with the diameter
The diameter is the width of the circle, which is measured starting from a point on the circumference, and ending on the opposite side through the center of the circle.
When you have to calculate the area if the diameter is given , it is as easy as before. The diameter is twice the radius, or what is the same, the radius is half the diameter.
D = 2r r = D/2
Therefore, when you have the diameter, you just have to convert it to the radius and reapply the original area formula. Let’s see an example with a circle of 8 cm in diameter:
r = 8/2 = 4 cm radius.
A = Π x 4 2 = Π x 16 = 50.24 cm2
You can also use the following formula that uses the diameter value instead of the radius:
Area = (Π/4) x D 2
A = (Π/4) x 8 2 = (Π/4) x 64 = 0.785 x 64 = 50.24 cm2
Calculation of the area of a circle with the circumference
As in the case of the diameter, we can find out from the circumference the radius, being C the circumference, which is equal to Π multiplied by the diameter:
C = Π x D
Since the diameter is worth twice the value of the radius, we can substitute:
C = Π x 2r
If we now redo the formula to isolate the radius we have:
r = C/2Π
But you can also use the value of the circumference by directly applying the following formula:
A = C 2 /4Π
This new formula comes from substituting the radius for the circumference in the original. We have the original formula: A = Π xr 2
And we substitute the radius: A = Π x (C/2Π) 2
We square the fraction: A = Π x (C 2 /2 2 Π 2 )
And we cancel the number Π in the numerator and denominator: A = Π x C 2 /4Π
Let’s apply it in an example, with a circle with a circumference of 50 cm. First we are going to deduce the radius using the relationship between the circumference and the radius:
r = 50/2Π = 50/6.28 = 7.96 cm radius.
Now we just have to apply the original area formula:
A = Π x 7.96 2 = Π x 63.37 = 199 cm 2 approximately.
If we use the formula that applies the value of the circumference directly, we have:
A = 50 2 /4Π = 2500/12.56 = 199 cm 2 approximately.