High School Polar to Rectangular Coordinate Converter
Convert coordinates from the Polar system (r, θ) to the Cartesian system (x, y).
Input Polar Coordinates
Rectangular Result
Coordinate x
Coordinate y
Calculation Steps:
Graph Visualization
Using the Polar to Rectangular Coordinate Converter
Navigating between different coordinate systems is a vital skill in physics, engineering, and mathematics. While the Cartesian system (rectangular) uses a grid of horizontal and vertical lines ($x, y$) to locate a point, the Polar system uses a distance from a central point and an angle ($r, \theta$).
The Conversion Formulas
To transform a point from polar to rectangular form, we use basic right-triangle trigonometry. Imagine the radius r is the hypotenuse of a triangle. The x coordinate corresponds to the adjacent side, and the y coordinate corresponds to the opposite side.
Simply plug in your radius and angle to find the horizontal and vertical components.
Why use a Polar to Rectangular Coordinate Converter?
In real-world scenarios like radar tracking or robotic arm movement, data often comes in polar form (distance and direction). However, to perform calculations like finding the distance between two objects or plotting on a computer screen, we often need to convert this data into rectangular $(x, y)$ coordinates. This tool automates that process, handling the trigonometric calculations and unit conversions (degrees/radians) instantly.
FAQ
Yes, this is a free educational resource available for students and teachers.
Mathematically, a negative radius implies measuring the distance in the opposite direction of the angle $\theta$. This tool accepts negative values and calculates the coordinates correctly.
Yes. You can toggle between Degrees and Radians using the dropdown menu next to the angle input.
The origin is the point $(0,0)$ in Cartesian coordinates or the “Pole” in Polar coordinates where $r=0$.