Circle Area Calculator: Calculator, Formulas and Examples

Area is a numerical characteristic of a two-dimensional (flat or curved) geometric figure, informally speaking, showing the size of this figure. Historically, the calculation of the area was called quadrature. A figure having an area is called quadratic. Find the area of more than 22 shapes (triangle, square, pentagon, etc.) using our amazing calculator.

Circle — is a part of a plane lying inside a circle. In other words, this is the geometrical location of the points of the plane, the distance from which to a given point, called the center of the circle, does not exceed a given non-negative number. The number is called the radius of this circle. If the radius is zero, then the circle degenerates to a point.

Knowing how to calculate the area of a circle is a fundamental skill in math and geometry. Our Circle Area Calculator simplifies the process of finding the area of a circle using various measurement methods. In this comprehensive guide, we will explain the Circle Area Formulas, demonstrate how to use the Circle Area Calculator, and provide practical examples to help you grasp the concept with ease.

How to Use the Circle Area Calculator

Our calculator makes it easy to find the area of a circle using different methods. To use the calculator:

1. Select the method you want to use: by radius, by diameter, by circumference, or by sector area.
2. Enter the required values (radius - r, diameter - d, circumference - P, sector area - Sₛₑ, sector angle - α) in coresponding fields.
3. That's it, our calculator will automaticaly give you the area of your rectangle with formula.

Circle Area Formulas

There are different ways to calculate the area of a circle. Here are the formulas for finding the area of a circle using different methods:

Circle Area by Radius

The formula for finding the area of a circle by radius is:

S = \pi r^2

• S - circle area
• π - constant that is the ratio of a circle's circumference to its diameter, approximately equal to 3.14159
• r - radius of the circle

This formula comes from the fact that the area of a circle is equal to the product of pi (π) and the square of the radius (r).

Circle Area by Diameter

The formula for finding the area of a circle by diameter is:

S = \dfrac{\pi d^2}{4}

Where:

• S - circel area
• d - diameter of the circel
• π - constant, approximately equal to 3.14159

Since the diameter of the circle is equal to twice the radius, by simple substitutions we obtain that the area of the circle is equal to the quart of the product of the square of the diameter and the number pi (π = 3.1415).

Circle Area by Circumference

The formula for finding the area of a circle by circumference is:

S = \dfrac{P^2}{4\pi}

Where:

• S - circel area
• P - circumference of the circel
• π - constant (≈3.14159)

The circumference is a double product of the radius and the number pi (π): P = 2πr, by the inverse method we get that the radius is equal to the length of the circle divided by its coefficient; hence, by substitutions, we can calculate the area of the circle.

Circle Area by the Sector Area

The formula for finding the area of a circle by sector area is:

S = S_{se}\dfrac{360}{\alpha}

Where:

• S - circel area
• α - central angle
• Sₛₑ - circle sector area

When you know the area of a sector and the measurement of the central angle, the area of the circle will be equal to the product of the area of the segment and 360 degrees divided by the central angle in degrees.

Circle Area Examples

Here are some examples of finding the area of a circle using different methods:

Example 1:

Find the area of a circle with a radius of 5 units.

S = \dfrac{\pi5^2}{2} = 78.54

Example 2:

Find the area of a circle with a diameter of 12 units.

S = \dfrac{\pi12^2}{4} = 113.10

Example 3:

Find the area of a circle with a circumference of 20 units.

S = \dfrac{20^2}{4\pi} = 31.83

Example 4:

Find the area of a circle with a sector angle of 120 degrees and a area of 60 units.

S = 60\dfrac{360^0}{60^0} = 180

Conclusion

Calculating the area of a circle is an important skill in math and geometry. Our Circle Area Calculator and formulas make it easy to find the area of a circle using different methods. Try it out for yourself and see how easy it can be!