Polar Distance Calculator - Calculator Academy

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.

D_{polar}=\sqrt{r1^2+r2^2-2*r1*r2*\cos(\theta_2-\theta_1)}

Where D_polar is the Polar Distance
r1,r2 are the radii (r1,r2)
θ1,θ2 are the angles (θ1,θ2) (in the same unit: degrees or radians)

How to Calculate Polar Distance?

The following example problems outline how to calculate Polar Distance.

Example Problem #1:

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

D_polar = √(r1² + r2² − 2·r1·r2·cos(θ2 − θ1))

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

D_polar = √(5² + 10² − 2·5·10·cos(50° − 30°)) = √(31.03) = 5.57

FAQ

What is Polar Distance?
Polar Distance refers to the distance between two points in a polar coordinate system, calculated using the radii and angles of these points relative to a common origin.

How does the Polar Distance formula work?
The Polar Distance formula uses the law of cosines: it computes r₁² + r₂² − 2r₁r₂cos(θ₂ − θ₁) and then takes the square root to get the actual distance.

Can the Polar Distance formula be used for any two points?
Yes, as long as the points are defined in polar coordinates (with a radius and an angle), the Polar Distance formula can be used to calculate the distance between them, regardless of their position.