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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.