Enter the radii (r1,r2) and the angles (θ1,θ2) into the Polar Distance Calculator. The calculator will evaluate and display the Polar Distance. 

Polar Distance Formula

The following formula is used to calculate the Polar Distance. 

Dpolar = r1^2+r2^2 – 2*r1*r2*cos(θ2-θ1)

  • Where Dpolar is the Polar Distance
  • r1,r2 are the radii (r1,r2) 
  • θ1,θ2 are the angles (θ1,θ2) (deg)

How to Calculate Polar Distance?

The following example problems outline how to calculate Polar Distance.

Example Problem #1:

  1. First, determine the radii (r1,r2). 
    • The radii (r1,r2) is given as: 5,10.
  2. Next, determine the angles (θ1,θ2). 
    • The angles (θ1,θ2) is provided as: 30,50.
  3. Finally, calculate the Polar Distance using the equation above: 

Dpolar = r1^2+r2^2 – 2*r1*r2*cos(θ2-θ1)

The values given above are inserted into the equation below and the solution is calculated:

Dpolar = 5^2+10^2 – 2*5*10*cos(50deg-30deg) = 31.03

Example Problem #2: 

For this problem, the variables needed are provided below:

radii (r1,r2) = 6,7

angles (θ1,θ2) = 20,50

This example problem is a test of your knowledge on the subject. Use the calculator above to check your answer. 

Dpolar = r1^2+r2^2 – 2*r1*r2*cos(θ2-θ1) = ?