Polar and X-Y, both directions
Drawings and machines speak two languages for the same point. A print may call out a feature as a radius and an angle from a datum; a mill or DRO wants it as X and Y. This calculator converts either way, with an optional pole offset so you can work from any datum rather than just the origin.
The conversions
Polar to rectangular: X = pole X + radius x cos(angle), Y = pole Y + radius x sin(angle). Rectangular to polar: radius = square root of (dX squared + dY squared), and angle = atan2(dY, dX), where dX and dY are measured from the pole. The result is normalized to a 0 to 360 degree bearing.
Why the pole matters
Set the pole to your part datum and a polar callout converts straight into machine coordinates, or an X-Y reading converts into the radius and angle a drawing expects. Leave it at zero to work from the part origin.
Related layout tools
To place holes evenly around a circle, use the bolt circle calculator; for a grid or row of holes, the hole pattern calculator. Both rely on the same polar-to-rectangular step this tool performs.
Worked example
A point 2 units out at 30 degrees from the origin lands at X = 2 cos 30 = 1.7321, Y = 2 sin 30 = 1.0000. Read it back the other way and 1.7321, 1.0000 returns a radius of 2 at 30 degrees.
FAQ
Which way do angles run?
Zero degrees points along positive X, and angles increase counterclockwise, matching standard math and most CAD. If your machine measures clockwise, enter the negative or the 360 complement of the angle.
What does atan2 do that plain arctangent does not?
It uses the signs of both X and Y to place the angle in the correct quadrant, so a point in the lower left returns a bearing near 200 degrees rather than collapsing onto the first quadrant.