Angle reference
The equations are X = R cos θ and Y = R sin θ. At 0° the point lies on +X; at 90°, on +Y; at 180°, on −X. Convert a drawing's clockwise or +Y-based angle to this reference before entering it.
Polar to Cartesian coordinate calculator
Convert polar coordinates (radius and angle) to Cartesian X/Y. Add a centre offset and copy positions, with examples of quadrants and CNC axes.
Polar → X/Y
0° = +X axis. For full bolt patterns use the hole circle (PCD).
1Enter the measurements
2Is the pattern center not the part zero?· add its position (leave at 0 if they match)
3Result
Click a dimension to copy it
Line for the program
X43.301 Y25.How to use this calculation
Convert a drawing point defined by radius and angle into X/Y coordinates. The calculator measures 0° along +X, with positive angles counterclockwise. Add a centre offset when the polar dimensions do not start at work zero.
Worked example
Known measurements
Radius R = 50 mm · angle = 30° · centre X0 = 10 mm, Y0 = 20 mm
Result
Local X ≈ 43.301 mm · local Y = 25 mm · absolute point ≈ X53.301 Y45
Add the centre after converting the polar point. Radius and centre offsets must use the same length unit.
Adding the pattern centre
Local coordinates are relative to the radius centre. With centre X0/Y0, the absolute point is X0 + X, Y0 + Y. Check whether your program uses absolute or incremental coordinates before copying a positioning line.
A single point or a bolt circle
This tool converts one polar position. For equally spaced holes, use the PCD calculator to set hole count, starting angle and direction. On a lathe, do not automatically interpret these planar coordinates as diameter-programmed X.
Frequently asked questions
Where does the angle start?
At +X, increasing counterclockwise. An angle of 90° points along +Y.
Why are some coordinates negative?
Signs depend on the quadrant. At 180°, for example, X = −R and Y = 0 relative to the centre.
What if the centre is not zero?
Add X0 to local X and Y0 to local Y to obtain the absolute position relative to that origin.
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