Polar to Cartesian Coordinates Converter

Transform polar coordinates (radius and angle) into Cartesian coordinates (x, y) with ease. Visualize the conversion and copy results instantly.

Enter the polar coordinates to convert them into Cartesian coordinates. Ensure the angle is provided in radians for accurate conversion.

Radius (r)

units

Angle (θ) in Radians

rad

Cartesian Coordinates:

X Coordinate (x):

Y Coordinate (y):

Coordinate Visualization

Understanding Polar to Cartesian Coordinates

In mathematics, there are two primary coordinate systems to locate points on a 2D plane: Polar and Cartesian.

Polar Coordinates: Define a point using a radius (r), which is the distance from a central point (origin or pole), and an angle (θ), measured counterclockwise from a reference direction (positive x-axis). A point P in polar coordinates is represented as (r, θ).

Cartesian Coordinates: Define a point using horizontal (x) and vertical (y) distances from the origin. These are perpendicular axes. A point P in Cartesian coordinates is represented as (x, y).

Conversion Formulas: To convert from polar (r, θ) to Cartesian (x, y), we use trigonometric relationships:

x = r * cos(θ)
y = r * sin(θ)

This tool simplifies this conversion by allowing you to input the radius and angle, and instantly get the Cartesian coordinates, along with a visual representation on a coordinate plane. It's useful in various fields like physics, engineering, and computer graphics for coordinate transformations and calculations.