CNC Circular Interpolation: G02 & G03 Explained with Real Milling and Turning Examples

Circular interpolation — G02 and G03 — controls arc and circular motion in CNC machining.
These commands allow precise tool movement along curved paths for contours, fillets, and holes without defining hundreds of straight lines.

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📌 1. What Are G02 and G03?

Code	Motion Direction	Description
G02	Clockwise (CW)	Tool moves in a circular path clockwise
G03	Counterclockwise (CCW)	Tool moves counterclockwise

They can be programmed using radius (R) or center-point offsets (I, J, K).

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📌 2. Plane Selection (G17 / G18 / G19)

Circular motion occurs in a defined plane:

Code	Plane	Axes Used	Common Use
G17	XY plane	I, J	Milling (top view)
G18	XZ plane	I, K	Turning
G19	YZ plane	J, K	Side milling

Always ensure the correct plane (usually G17 for milling).

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📌 3. G02/G03 Using Radius (R Method)

G02 X50. Y50. R25. F200

Moves from current point to (X50, Y50) along a 25 mm radius arc, clockwise.

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📌 4. G02/G03 Using I, J (Center Offset Method)

G02 X50. Y50. I25. J0. F200

Parameter	Meaning
I	X distance from start to arc center
J	Y distance from start to arc center

CNC calculates arc geometry from these offsets.

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📌 5. Full Example — Clockwise Circular Milling (G02)

%
O9001 (G02 CLOCKWISE ARC)
G90 G17 G21 G40 G80 G54
T01 M06
S2000 M03
G00 X0 Y0 Z5.
G01 Z-5. F100
G02 X50. Y0. I25. J0. F250
G00 Z100.
M30
%

Cuts a 180° clockwise arc from X0,Y0 to X50,Y0 around a center at X25,Y0.

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📌 6. Counterclockwise Example — G03

G03 X50. Y0. I25. J0. F250

Same geometry, but tool moves counterclockwise around the arc.

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📌 7. Arc Quadrant Rules

When using R value:

• R positive → arc < 180°
• R negative → arc > 180°
• R value = arc radius (not diameter)

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📌 8. G02/G03 in Turning (G18 Plane)

Used to generate profiles and fillets on a lathe.

Example (Fanuc Lathe):

%
O9002 (LATHE ARC PROFILE)
G50 S2000
G97 S1200 M03
T0101
G00 X60. Z0.
G02 X40. Z-10. I-10. K0.
G03 X20. Z-20. I-10. K0.
G00 X100. Z100.
M30
%

Code	Description
I, K	Arc center relative to start point
G02	Clockwise profile
G03	Counterclockwise profile

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📌 9. G03 for Corner Fillets (Example)

G03 X60. Y60. R10.

Generates a smooth 10 mm radius corner fillet between two linear moves.

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📌 10. G02/G03 in Helical Interpolation (3D Arc)

Helical interpolation combines circular (G02/G03) and linear (Z) moves — ideal for thread milling and ramping.

Example:

%
O9003 (HELICAL INTERPOLATION)
G90 G17 G21 G40 G80 G54
T02 M06
S1500 M03
G00 X25. Y0. Z5.
G01 Z0. F100
G03 X25. Y0. I-25. J0. Z-10. F250
G00 Z100.
M30
%

Creates a spiral helix 10 mm deep while circling around a 25 mm radius.

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📌 11. Siemens Example

G02 X50 Y50 CR=25 F200

Siemens uses CR instead of R for radius-based arcs.

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📌 12. Heidenhain Example

CC X25 Y0
C X50 Y0 DR+

Command	Description
CC	Define circle center
C	Execute circular motion
DR+ / DR−	Direction (CW / CCW)

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📌 13. Common G02/G03 Geometry Mistakes

Mistake	Result
Wrong plane (G18 vs G17)	Arc goes in wrong direction
Missing I/J or R	Alarm: “No arc center defined”
Wrong R sign	Wrong sweep direction
Mixing I/J with R	Controller alarm
Inconsistent start/end geometry	“Non-tangent arc” error

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📌 14. Advanced Application — Circular Pocket Milling

%
O9010 (CIRCULAR POCKET)
G90 G17 G21 G40 G80 G54
T03 M06
S1800 M03
G00 X0 Y0 Z5.
G01 Z-2. F150
G03 X0 Y0 I25. J0. Z-10. F200
G00 Z100.
M30
%

Creates a 50 mm diameter circular pocket by spiraling downward using helical interpolation.

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📌 15. Calculating I, J (Arc Center Offsets)

Start	End	Center	I	J
(0,0)	(50,0)	(25,0)	+25	0
(0,0)	(0,50)	(0,25)	0	+25

I and J define the center relative to start point — not absolute coordinates.

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📌 16. Best Practices

• Always program G17 plane explicitly for milling.
• Use R for simple arcs, I/J for precise geometry.
• Ensure toolpath direction (CW vs CCW) matches contour.
• Keep feedrate constant across arc for uniform surface finish.
• Avoid over 180° arcs with R method — use I/J for reliability.

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📌 17. Future Trends (2025–2030)

• AI-based contour learning — CNC automatically determines G02/G03 parameters from DXF geometry.
• High-precision interpolation (NURBS) — smoother surface generation beyond circular paths.
• CAM-generated hybrid arcs — combining G02/G03 with spline motion for aerospace-grade accuracy.

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✅ Conclusion

Circular interpolation with G02 and G03 is the backbone of complex contour machining.
By understanding the geometry behind I, J, K and direction logic, CNC machinists can achieve perfect arcs, fillets, and helical paths — efficiently and precisely every time.