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) = ?