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Tools City

Area of a Circle Calculator

The area of a circle calculator helps to compute the surface of a circle given diameter or radius. Tools City's Area of circle calculator works both ways - no matter if you are looking for an area to radius calculator or a radius to the area one, you have found the right place.

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What is a Circle?

A circle is made up of points that are equidistant from the center of a circle. A closed geometric form is a circle. In everyday life, we see circles in the form of a wheel, rings, pizzas, around the ground, Etc.

What is Radius?

The distance between the centre of a circle and any other spot along its perimeter is the radius of a circle.

The letter 'r' or 'R' is used to express it. The formula for the area and circumference of a circle, which we shall learn later, involves radius.

What is the diameter of any circle?

The circle's diameter is explained as a line that starts from one point on the border, goes through the center point/origin, and ends on the circle's border. The letter 'd' or 'D' is used to symbolize it. We can also assume that when two radii meet, a diameter is made.

Which formula is used to figure out the diameter of the circle?

Circle diameter formula: A circle's diameter formula is twice its radius.

Diameter = 2 x radius

d = 2 x r

r = d/2 or d = 2 x r.

 

Which formula is used to figure out the radius of the circle?

If you already know the diameter of a circle and want to determine its radius. Then, we will be using the below formula for that: 

diameter = 2 x radius or D = 2 x R

What is the area of a circle?

The area of a circle refers to the amount of space contained inside a circle's border. The area filled by the circle is the region within the circle's perimeter. It is also known as the total amount of square units included within the circle.

A circle's area is the amount of space it takes up on a two-dimensional plane. Conversely, the space occupied inside the boundary or circumference of a circle is considered the area of a circle.

How can we measure the Area of any circle?

The formula which we use to figure out the area of a particular circle is written below:

Area = product between pi and the square of the radius 

A = πr2

Where,

  • A is called the area of the circle
  • Pi (π) is said to be the ratio of the circumference.
  • R is said to be the radius of a circle

The formula to determine the area of a circle if you are given the value of diameter is:

Area = product of pi and the square of the diameter divided by 4

A = πd2/4

Where,

  • A is said to be the area of the circle
  • Pi (π) is considered as the ratio of the circumference of a circle
  • d is the diameter of a circle

The area of a circle formula is used to determine the space occupied by a circular track of the plot. For example, if you have a table of circular shapes, and you want to determine its area to purchase cloth for it. Then this formula can be beneficial to determine how much cloth is required to cover it completely. 

How to use Tools City's Area of a Circle tool?

Using Tools City's Area of a Circle tool is as easy as a walk in the park. Just go to the Area of circle tool and enter the value that you have whether it is Area, Radius, or Diameter. Simply by entering the value the calculator will provide the results instantly.

You can also change the unit of your measurement into the below-mentioned units:

  • millimeters (mm)
  • centimeters (cm)
  • meters (m)
  • kilometers (km)
  • inches (in)
  • feet (ft)
  • yards (yd)
  • miles (mi)
  • nautical miles (nmi)

Can I do it manually?

Yes! You can easily do it by yourself by using the formulas displayed on the screen whenever you use this free tool.

To understand it more conveniently, let us have a look at these examples

Example 1: 

If the radius of a circular path is 40 mm. Calculate its area.

As we know the radius is 40 mm:

Using the formula for the area,

Area of a Circle = πr2

Now putting the value of Radius,

A = π x 402

A =π x 1600

A = 1600π ≈ 5027 mm2

Example 2: 

If the diameter of a circular park is 16 mm. Calculate its area.

As we know the diameter is 16 mm:

Using the formula for the area,

Area of a Circle = (π/4)×d2

Now putting the value of Diameter,

A = (π/4) × 162

A = (π/4) × 256

A = 64π ≈ 201.5 mm2