G2 & G3 Arcs: I, J, K vs R Format Explained

G2 cuts an arc clockwise, G3 counter-clockwise, from the current position to the endpoint given in the block. Direction is judged looking at the active plane from the positive side — for the default XY plane (G17), that's the view from above.

Every arc needs two things besides the endpoint: which plane it lives in (set by G17/G18/G19), and where its center is — given either as center offsets (I/J/K) or a radius (R).

#IJK format: center offsets

I, J, K are the distances from the start point to the arc center, measured along X, Y, Z. On nearly every control they are incremental by default, even in G90 absolute mode:

G17 G90              ; XY plane, absolute endpoints
G0 X10 Y0
G2 X0 Y10 I-10 J0 F400   ; quarter circle: center at (0,0), radius 10

Start (10,0), center = start + (I,J) = (0,0), end (0,10), clockwise — a 90° arc. Add a Z word and the arc becomes a helix, the standard way CAM ramps into a pocket:

G2 X10 Y0 I-10 J0 Z-2    ; full turn spiraling down 2 mm

A block whose endpoint equals its start point cuts a full circle in IJK format (Mach3/4 also offer G12/G13, which treat the current position as the center — nonstandard, avoid in portable code).

#R format: radius

G2 X0 Y10 R10 says "get there on a radius-10 arc." Shorter to write, but ambiguous: two arcs of the same radius connect any two points — a minor (<180°) and a major (>180°) one. Positive R picks the minor arc, negative R the major. Full circles are impossible in R format, and near-180° arcs amplify rounding error, which is why CAM posts overwhelmingly emit IJK.

#Common mistakes

• Wrong plane active. An arc programmed for XY while G18 is active either alarms or cuts a completely different curve. State G17 in the preamble; the plane matters even if you never cut in ZX or YZ.
• Absolute vs incremental centers. LinuxCNC, Mach and Centroid support G90.1 (absolute IJK). A program posted for absolute centers, run on a control expecting incremental ones, produces radius errors or wild arcs. If arcs look insane in simulation, this is the first suspect.
• Trusting R near 180°. Tiny endpoint rounding flips which arc R selects or fails the radius check. Use IJK for anything close to a half circle.
• Feeding arcs like lines. G2/G3 are feed moves — they need an active F, and on inside corners the effective tool-edge feed is higher than the programmed centerline feed. That's a machining detail, but it starts in the G-code.