Rectangular to Polar Conversion Calculator

Enter value and click on calculate. Result will be displayed.
For (x1, y1) and (x2, y2)
If (x1 > x2) then x = x1 - x2 else x = x2 - x1
If (y1 > y2) then y = y1 - y2 else y = y2 - y1
R = Sqrt(x2+y2)       Angle = tan -1(y/x)

Rectangular coordinates

X1:
Y1:
X2:
Y2:

Result: Polar Coordinates

R:
Angle:
deg

A Rectangular to Polar Conversion Calculator is a tool used to convert complex numbers or coordinates from rectangular (also known as Cartesian) form into polar form.

What is Rectangular and Polar Form?

  • Rectangular form (Cartesian coordinates) represents a point using two values: x(the horizontal component) and y(the vertical component). It’s usually written as (x,y), where xx and y are the real and imaginary parts of a complex number respectively, or the coordinates of a point in 2D space.

  • Polar form, on the other hand, represents a point in terms of its magnitude (r) and its angle (θ) with respect to the positive x-axis. The polar form is written as (r,θ), where:

    • is the distance from the origin (magnitude),
    • θ is the angle in radians or degrees.

Why Use Rectangular to Polar Conversion?

  • Complex Numbers: In the context of complex numbers, converting from rectangular to polar form makes it easier to perform certain operations like multiplication, division, and exponentiation.

  • Applications: In physics and engineering, especially in fields like electromagnetism, signal processing, and mechanics, polar coordinates simplify problems that involve rotations or waves, where magnitude and direction are more important than exact position.

How to Convert Rectangular to Polar Coordinates

To convert rectangular coordinates (x,y) to polar coordinates (r,θ), use the following formulas:

Example:

  • If you have the rectangular coordinates (x,y)=(3,4),

So, the polar form of the point (3,4) is (5,0.93) radians or (5,53.13∘).

When Would You Use This?

  • In engineering, particularly when dealing with circuits or waveforms.
  • In computer graphics when handling rotations or transformations.
  • In navigation and mapping where angles and distances from a reference point are more intuitive.

Rectangular-to-polar conversion can be done manually, but using a calculator or software tool makes the process faster and eliminates errors, especially when dealing with complex numbers or many conversions at once.