Rectangular to Polar Conversion Calculator

Enter value and click on calculate. Result will be displayed.
x value :
y value :
Result:
radius(r) :
θ (degrees) :
θ (radians) :

A Rectangular to Polar Conversion Calculator is a tool that converts coordinates from the rectangular (Cartesian) system — where points are defined by x- and y-coordinates — to the polar coordinate system, where points are defined by radius and angle.

Why use a Rectangular to Polar Conversion Calculator?

  • Simplifies Complex Numbers: Polar coordinates make it easier to work with complex numbers, trigonometry, and vector math.
  • Useful in Physics and Engineering: Many physical systems (like waves, circular motion, and electromagnetic fields) are easier to describe in polar form.
  • Easier Calculations for Rotation and Scaling: Polar coordinates simplify transformations like rotation and scaling.
  • Graphing Circular Patterns: When working with curves and shapes like circles and spirals, polar coordinates are often more intuitive.

How does a Rectangular to Polar Conversion Calculator work?
The calculator uses these formulas to convert the Cartesian coordinates (x, y) into polar coordinates (r,θ):

  • ​ — the distance from the origin (0, 0) to the point
  • — the angle from the positive x-axis to the point (in radians or degrees)

Input:

  • x-coordinate
  • y-coordinate

Calculation: It computes the radius rr r and the angle θ.

Output:

  • r: The distance from the origin to the point
  • θ: The angle in degrees or radians

When should you use a Rectangular to Polar Conversion Calculator?

  • In Trigonometry and Calculus: When working with curves and integrals in polar form.
  • For Electrical Engineering: Analyzing AC circuits often involves phasors, which use polar representation.
  • In Computer Graphics: Rotations and scaling transformations can be more efficient in polar form.
  • For Navigation and Robotics: Polar coordinates make sense for systems based on angles and distances from a fixed point.