Tool path radius calculator: compensation for internal and external contours
Calculate the corrected path radius for the tool centre point on circular contours. Path correction — also known as tool radius correction or cutter radius compensation — prevents the most common programming error in circular pockets and islands: programming the nominal radius directly instead of the corrected path radius. For internal contours, the tool radius is subtracted; for external contours, it is added.
Contour and tool path
Milling tools in the shop90 items
Note: All values are non-binding reference figures. Actual values depend on machine, tool, material and conditions. Start conservatively. No liability is accepted for tool breakage, machine damage or machining results.
What the Path Radius Calculator Computes
For circular contours, it is not the tool centre that mills the programmed radius, but the cutter edge. To ensure the component ultimately has the desired target radius, the tool centre point (i.e. the programmed path) must be corrected by the tool radius. The calculator determines this corrected path radius for internal contours (pockets, bores) and external contours (islands, outer edges).
The Formula
Internal contour: rpath = Rtarget − rtool
External contour: rpath = Rtarget + rtool
For an internal pocket, the cutter edge is further out than the tool centre. The path must therefore be tighter than the target radius. For an external contour, it is the reverse: the cutter edge lies further in than the tool centre, so the path must be wider. Example internal pocket: target radius 20 mm, 6 mm cutter (radius 3 mm) → path radius = 20 − 3 = 17 mm.
Important: When the Tool Does Not Fit
For internal contours, there is a hard limit: the tool radius must be smaller than the target radius. If the cutter is the same size or larger, it does not geometrically fit into the pocket. The calculator reports this explicitly rather than outputting a false or negative path radius. For external contours, this restriction does not apply: any tool can traverse an external contour, regardless of its size.
Why This Matters in Practice
- CAM software usually handles this automatically: When programming with CAM software, you enter the target radius and tool diameter directly. The software calculates the compensation itself. The calculator helps for verification or when programming by hand (direct G-code).
- Checking before machining: Even with CAM software, a quick check is worthwhile to see whether the selected tool geometrically fits the smallest internal contour of the component at all, before the machine runs.
- Manual G-code programming: For simple circular pockets or bores without CAM, the corrected radius can be entered directly into the G02/G03 command.
Frequently Asked Questions
Why is it not enough simply to program the target radius?
The CNC controller moves the tool centre point, not the cutting edge. If you programmed the target radius directly for an internal pocket, the cutter edge would mill the radius too large by the full tool radius. The pocket would be too wide. Therefore, the path for the centre point must be programmed correspondingly tighter (internal) or wider (external).
What happens if I choose a tool that is too large for an internal pocket?
Geometrically, the cutter then does not fit into the pocket. The calculated path would become negative or zero, which makes no sense. In practice, you would need a slimmer tool or would have to design the pocket larger. The calculator recognises this case and explicitly points it out instead of displaying an incorrect result.
Does the CAM software not do this automatically anyway?
Yes, modern CAM software handles tool radius compensation automatically when the target contour and tool diameter are entered. The calculator is nevertheless useful: for a quick plausibility check, for manual G-code programming without CAM, or to check in advance whether a tool is suitable for the tightest point of a component.
Does the formula also apply to circular arcs that are not full circles?
Yes, tool radius compensation works for circular arcs just as it does for full circles. What matters is only the local radius of the contour at the respective point, not whether it is a full circle.
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