G2 G3 R Value – CNC Course (12) Arcs & The Difference Between R+ and R-
Video
Overview
The G2 G3 R value is one of the most misunderstood concepts in manual arc programming — and this demonstration makes it visual. Both R+ and R− share the same two endpoints and the same radius. The sign is the only difference, and it determines which of two possible arcs the machine cuts. You’ll see both side by side to understand the geometry for yourself before applying the rule in a real program.
The lesson also introduces the figure-8 toolpath — a demonstration of what chained arcs can do. Two lines of G-code, one shape, and an understanding of the G2 G3 R value rule locked in for good.
What You’ll Learn
- How the G2 G3 R value sign determines which of two possible arcs gets cut
- The difference between a positive R (minor arc, ≤ 180°) and a negative R (major arc, > 180°)
- How to program R+ and R− arcs using G2 and G3
- How to create a figure-8 toolpath from two chained major arcs
- When the R method works best — and where it does not
G2 G3 R Value Explained
- R+ — Positive R selects the minor arc: the short path between two points, up to and including 180°
- R− — Negative R selects the major arc: the long path between the same two points, sweeping > 180°
- G2 — Clockwise arc direction; works with both positive and negative R
- G3 — Counter-clockwise arc direction; works with both positive and negative R
- Figure-8 toolpath — Two major arcs (R−) chained with alternating G2 and G3 direction, each looping back to the same start point
- I/J method — Center-offset arc programming; required for reliable full 360° circles where R is undefined
Project Notes
- R sign and arc direction (G2 vs G3) are independent choices — both must be correct to get the arc you want.
- A negative R surprises most beginners: the toolpath goes in a completely different direction than expected. Use a program like NCViewer to simulate the results before running on the machine.
- The figure-8 uses coincident start and end points with negative R. Behavior can vary between GRBL versions.
- R cannot reliably program a simple full 360° circle. When start equals end point, many GRBL versions return an error. Use I/J for full circles instead.
- This technique works on any GRBL-based machine running firmware v1.1 or later.
Tools & Materials
- 3018-style CNC router (or any GRBL-based machine)
- Candle (GRBL Control) — free CNC sender: github.com/Denvi/Candle
- GRBL firmware v1.1+
- Text editor (Notepad, VS Code, or similar)
- NCViewer — free online G-code simulator: ncviewer.com
G-Code Snippet (Simplified Example)
(Not an exact copy from the video)
G17 G21 G90 ; setup: XY plane, metric, absolute
G2 X10 Y0 R5 F400 ; CW minor arc — R+ (short route)
G2 X10 Y0 R-5 F400 ; CW major arc — R- (long route)
G2 X0 Y0 R-10 F400 ; figure-8: loop 1 (CW, major arc)
G3 X0 Y0 R-10 F400 ; figure-8: loop 2 (CCW, major arc)
Watch the Lesson
This short video demonstrates the G2 G3 R value by putting R+ and R− arcs side by side using identical endpoints. You can see exactly why one sign takes the short route and the other takes the long route.