KEVOS® MAKEOS · Geometry
Polar and Rectangular Coordinates
What are the X–Y coordinates of this radius and angle, or the radius and angle of this X–Y point?
Convert a point between polar (radius and angle) and rectangular (X and Y) coordinates about a chosen origin, for hole positions and CNC programming.
Open the calculatorRuns in your browser. No account needed.
How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Convert | choice | Direction of conversion. |
| Radius | mm | Distance from the origin (used for radius and angle → X and Y). |
| Angle from +X axis (anticlockwise) | ° | Angle measured anticlockwise from the positive X axis; negative is clockwise. |
| X | mm | X coordinate from the origin (used for X and Y → radius and angle). |
| Y | mm | Y coordinate from the origin. |
Method and formulas
- X = r cos θ; Y = r sin θ.
- r = √(X² + Y²); θ = atan2(Y, X), reported from 0° to 360°.
- Example: a radius of 50 mm at 30° is X = 43.301 mm, Y = 25 mm.
Limitations
- Angles follow the mathematical convention (anticlockwise from +X); some machine controls and drawings measure differently.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Program a hole at a radius and angle
- Check a measured XY position against a polar callout
- Convert inspection data
Who it is for
- CNC programmers
- Quality inspectors
- Toolmakers
What you get
- X and Y
- Radius
- Angle (0–360°)
Interpreting the result
- Confirm the angle zero and direction against the drawing before programming.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 43–45, 692–694. Topic reference; no source tables or recommended settings are reproduced.
WORKOS tools are screening and decision-support utilities. Verify important financial, engineering, safety, legal or operational decisions using appropriate professional standards and your organisation’s approved data.
