Polar to Rectangular Converter: r, θ
This polar and rectangular coordinates converter changes a point between the two systems. Choose polar to rectangular, enter the radius r and the angle θ, and get x = r cos θ and y = r sin θ. Choose rectangular to polar, enter x and y, and get the distance r = √(x² + y²) and the angle θ from atan2, so the angle is placed in the correct quadrant. You can work in degrees or radians, and the result shows the angle in both, plus the equivalent range from 0 to 360° and from −180° to 180°. It is handy for trigonometry, physics vectors, complex numbers and engineering homework.
Polar and Rectangular Coordinates Converter
Convert polar coordinates (r, θ) to rectangular (x, y) and back. Degrees or radians, with quadrant and exact angles.
How to use the Polar and Rectangular Coordinates Converter
- Pick polar to rectangular or rectangular to polar.
- Choose degrees or radians for the angle.
- Enter r and θ, or x and y.
- Read the converted point, the quadrant and the angle in both units.
Features
- Both directions in one tool
- Degrees and radians
- Uses atan2 so the quadrant is always right
- Angle shown as 0 to 360 and as −180 to 180
- Handles negative radius and the origin
- Copy the result
Frequently asked questions
How do you convert polar to rectangular coordinates?
Use x = r cos θ and y = r sin θ. For r = 2 and θ = 60° this gives x = 1 and y = 1.732.
How do you convert rectangular to polar coordinates?
Find r = √(x² + y²) and θ = atan2(y, x). Using atan2 instead of a plain arctangent puts the angle in the right quadrant.
What is the difference between degrees and radians?
A full turn is 360 degrees or 2π radians, so 180° equals π radians and 1 radian is about 57.2958°.
Can r be negative?
Yes. A negative r points in the opposite direction, so (−2, 30°) is the same point as (2, 210°). The converter handles it.
What is the angle of the origin?
The origin (0, 0) has r = 0 and no single angle, so the tool shows 0 and notes that the angle has no defined value.