What is the formula for calculating the area of a circle?

What is a circle?

In plane geometry, a circle is the set of all points equidistant from a fixed point (called the center) with a specified distance called the radius.

The radius of the circle must be a positive number, greater than 0.

How is a circle different from a circle?

Circle and circle are two different concepts.

A circle is the set of all points that lie inside and on the circle. In other words, a circle is a cross-section and therefore has an area.

A circle is the locus of all points on a plane equidistant from a given point (called the center) - a closed curve (such as a contour, boundary) has no area.

Formula for calculating the area of a circle

The area of a circle is calculated by multiplying the square of the radius by pi.

S = rxrxnbsp;π = r ² x π

In there:

S: Area of a circle

r: Radius of a circle - is the distance from the center of the circle to any point on the circle.

π (pi): The number pi is a mathematical constant, approximately equal to 3.14159

How to calculate the area of a circle when knowing the diameter

In mathematics and geometry, a diameter is a line segment that passes through the center of a circle and connects any two points on the circle. The diameter is the longest line segment in a circle, dividing the circle into two equal halves and having a length twice the radius.

For problems with only diameter data, use the formula for calculating the area of a circle by the square of ½ the diameter multiplied by pi.

S = (d/2) ² x π

In there:

S: Area of a circle

d: Length of circle diameter

π (pi): The number pi is a mathematical constant, approximately equal to 3.14159

How to calculate the area of a circle when knowing the circumference

The circumference of a circle is the length of the path around the circle. The formula for calculating the circumference (C) is C = π xd (where d is the diameter) or C = 2 xrx π (where r is the radius).

For problems with only circumference data, there are two ways to calculate the area of a circle.

Method 1: Using the general formula:

S = r ² x π

- Step 1: Find the radius (r) from the circumference (C)

The circumference of a circle is C = 2 xrx π so r =C/(2π)

- Step 2: Apply the formula to calculate the area of a circle

The area of a circle is S = r ² x π. Substitute the new r found in step 1 to get: S = (C/2π)² x π

After simplifying we get the final formula: S = (C) ² /4π.

Method 2: Apply the simplified formula to calculate the area of a circle by dividing the square of the circumference by 4 times pi:

S = (C) ² / 4π

In there:

S: Area of a circle