Formula for Area of a Circle

The formula for area of a circle is one of the most useful formula in math. The formula of area of a circle allows you to calculate the area of a circle very quickly. Proving the formula of area of a circle is left to college level math. The formula for area of a circle is not the same as the formula for the surface area of a circle which we shall discuss later. We will discuss formula for circumference and area of a circle in this section.

The formula for area of a circle uses two mathematical elements:

• the radius of the circle, and
• pi

The radius of a circle is the distance between the midpoint of the circle and the circumference of the circle. The radius of a circle is the same no matter where on the circumference of the circle you measure from. In the circle below, the radius of the circle is denoted by 'r'. All the lines denoted by r are of the same length so it does not matter where you measure the r to as long as it is from the mid point of the circle.

Formula for Area of a Circle

The formula for area of a circle is given by:

The above formula to find area of a circle works for any radius r. Pi in the area of circle equation above is roughly 3.14159265

Formula for circumference of a Circle

The formula for the circumference of a circle is the same as the formula for the perimeter of a circle and is given by:

Now you can use the formula for area of a circle to calculate the area of a circle and the formula for the circumference of a circle to calculate the perimeter or circumference of a circle. The formula for the circumference of a circle is sometimes denoted by  x d where d is the diameter of the circle. Since d = 2r the two formulas for the circumference of a circle is essentially the same.