Enter the polar angle (degrees) and the polar radius into the Polar Area Calculator. The calculator will evaluate the Polar Area. 

Polar Area Formula

The following two example problems outline the steps and information needed to calculate the Polar Area.

PA = 1/2 * (a/57.2958) * r^2
  • Where PA is the Polar Area
  • a is the polar angle (degrees) 
  • r is the polar radius 

To calculate the polar area, multiply the angle in radians by the radius squared, then divide by 2.

How to Calculate Polar Area?

The following example problems outline how to calculate Polar Area.

Example Problem #1:

  1. First, determine the polar angle (degrees).
    • The polar angle (degrees) is given as: 30.
  2. Next, determine the polar radius.
    • The polar radius is provided as: 5.
  3. Finally, calculate the Polar Area using the equation above: 

PA = 1/2 * a * r^2

The values provided above are inserted into the equation below and computed.

PA = 1/2 * (30/57.2958) * 5^2 = 6.54


Example Problem #2: 

For this problem, the variables required are provided below:

polar angle (degrees) = 6

polar radius = 30

Test your knowledge using the equation and check your answer with the calculator.

PA = 1/2 * a * r^2 = ?