THE NUMORIX GUIDE
How to use the Polar/Rectangular Converter
Last reviewed September 14, 2026
What this calculator does
Rectangular-to-polar uses r=sqrt(x^2+y^2) and theta=atan2(y,x).
Formula and method
Rectangular-to-polar uses r=sqrt(x^2+y^2) and theta=atan2(y,x). Polar-to-rectangular treats x as r and y as a degree angle, then uses rectangular x=r*cos(theta), y=r*sin(theta).
Variables and inputs
Direction defaults to Rectangular to Polar with x=3 and y=4. In reverse mode the first field is r and the second is theta in degrees.
Worked example
For (x,y)=(3,4): r=sqrt(9+16)=5; theta=atan2(4,3)=0.9273 radians = 53.13 degrees. Reversing r=5 and theta=53.13 degrees returns approximately (3,4).
How to interpret the result
Rectangular coordinates give horizontal and vertical components; polar coordinates give distance from the origin and direction.
Common mistakes to avoid
Use atan2 rather than atan(y/x) so the quadrant is preserved. In polar-to-rectangular mode, enter the angle in degrees because the UI label says degrees.
Assumptions and limitations
The reverse branch uses degrees only and the polar angle is not unique because adding 360 degrees gives the same point. Floating-point trigonometry leaves tiny residuals near zero.
Practical use and checks
The Polar/Rectangular Converter changes a two-dimensional point between Cartesian components and radius-angle form. In rectangular-to-polar mode, enter x = 3 and y = 4 as a check; radius should be 5 and angle should be about 53.13 degrees, or 0.9273 radians. In polar-to-rectangular mode, enter radius 5 and angle 53.1301 degrees; the components should return close to x = 3 and y = 4. Use the radius for magnitude and the angle for direction from the positive x-axis. The atan2 calculation preserves the quadrant, so a point with x negative should not be converted with a one-argument arctangent that loses its direction. Make sure the polar input's first field is a nonnegative radius and the second field is an angle in degrees when that mode is selected. Angles differing by 360 degrees describe the same direction, and radius zero has no unique angle even though a numerical angle may be returned. The tool is two-dimensional and does not handle elevation, branch conventions, or unit conversion. Rounding can make a round trip return 2.9999 instead of 3. For navigation, engineering, or signal work, state the axis convention and angle orientation next to the result so a correct number is not applied with the wrong reference direction.