Polar Area Calculator

Formula

To calculate the Polar Area (PA):

\[ PA = \frac{1}{2} \times \left(\frac{a}{57.2958}\right) \times r^2 \]

Where:

\(PA\) is the Polar Area
\(a\) is the polar angle (degrees)
\(r\) is the polar radius

What is a Polar Area?

The polar area is the area swept out by a radius vector as it rotates through an angle in a polar coordinate system. The formula provided calculates this area given a specific angle and radius.

Example Calculation 1

Let's assume the following values:

Polar Angle (\(a\)) = 60 degrees
Polar Radius (\(r\)) = 5 units

Using the formula:

Step 1: Convert the angle to radians:

\[ a_{rad} = \frac{60}{57.2958} = 1.0472 \, radians \]

Step 2: Calculate the Polar Area:

\[ PA = \frac{1}{2} \times 1.0472 \times 5^2 = 13.09 \, square \, units \]

The Polar Area is 13.09 square units.

Example Calculation 2

Let's assume the following values:

Polar Angle (\(a\)) = 90 degrees
Polar Radius (\(r\)) = 3 units

Using the formula:

Step 1: Convert the angle to radians:

\[ a_{rad} = \frac{90}{57.2958} = 1.5708 \, radians \]

Step 2: Calculate the Polar Area:

\[ PA = \frac{1}{2} \times 1.5708 \times 3^2 = 7.07 \, square \, units \]

The Polar Area is 7.07 square units.