Polar to Rectangular Calculator
Convert between polar and rectangular coordinate systems in either direction. Enter polar coordinates (r, theta) to get (x, y), or enter rectangular coordinates (x, y) to get (r, theta). For example, the polar point (5, 53.13 degrees) converts to approximately (3, 4) in rectangular form.
Polar to Rectangular Conversion
Given polar coordinates (r, theta):
- x = r x cos(theta)
- y = r x sin(theta)
Example: Convert (10, 60 degrees) to rectangular.
- x = 10 x cos(60) = 10 x 0.5 = 5
- y = 10 x sin(60) = 10 x 0.866 = 8.66
- Result: (5, 8.66)
Rectangular to Polar Conversion
Given rectangular coordinates (x, y):
- r = sqrt(x^2 + y^2)
- theta = atan2(y, x)
Example: Convert (3, 4) to polar.
- r = sqrt(9 + 16) = sqrt(25) = 5
- theta = atan2(4, 3) = 53.13 degrees
- Result: (5, 53.13 degrees)
Degrees vs. Radians
This calculator supports both angle units. To convert between them:
- Degrees to radians: multiply by pi/180
- Radians to degrees: multiply by 180/pi
Common angles: 90 degrees = pi/2 radians, 180 degrees = pi radians, 360 degrees = 2pi radians.
When to Use Each System
- Rectangular (x, y): Best for straight lines, linear algebra, and Cartesian problems
- Polar (r, theta): Best for circles, spirals, rotations, and problems with radial symmetry