Polar to Cartesian Coordinate Converter
Convert between polar coordinates (r, theta) and Cartesian coordinates (x, y).
Supports degrees and radians.
Two Coordinate Systems Cartesian coordinates locate a point using horizontal (x) and vertical (y) distances from the origin. Polar coordinates locate the same point using distance from the origin (r) and angle from the positive x-axis (theta). Both systems describe the same plane, but some problems are much easier in one system than the other.
Polar to Cartesian x = r * cos(theta). y = r * sin(theta). For example, (r=5, theta=30 degrees) gives x = 5cos(30) = 4.33 and y = 5sin(30) = 2.5.
Cartesian to Polar r = sqrt(x^2 + y^2). theta = atan2(y, x). The atan2 function correctly handles all four quadrants, unlike basic arctan which only covers two.
Radians vs Degrees Radians are the natural unit for angles in mathematics: a full circle is 2*pi radians (approximately 6.2832). Degrees are the everyday unit: a full circle is 360 degrees. To convert: radians = degrees * pi / 180. Common angles: 30 degrees = pi/6, 45 degrees = pi/4, 60 degrees = pi/3, 90 degrees = pi/2.
When to Use Each System Polar coordinates simplify problems involving circles, spirals, and rotational symmetry. Cartesian coordinates are better for lines, rectangles, and translations. Many physics problems (planetary orbits, electromagnetic fields, wave functions) are naturally expressed in polar or cylindrical coordinates.