TiAlN coating benefits for carbide tools. Get instant I (mm), J (mm), Arc Center X,Y for your machining parameters.
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Request a Proposal →Every seasoned CNC machinist knows that getting the numbers right means the difference between scrap and a perfect part. Arc R to IJ Converter is no exception. When Widia application engineers walk a customer through process optimization, this is one of the first parameters they check — because even a 5% error here can cascade into tool failure or out-of-tolerance parts.
The formula at work here is deceptively simple but carries deep implications. Kyocera publishes reference tables for this parameter across their full turning and milling catalog, and Korloy integrates it directly into their ToolGuide app. The underlying principle hasn't changed in decades, but modern coated carbides have pushed the usable range significantly.
Always cross-reference your calculated values against your tool manufacturer's recommended ranges. Widia's CoroPlus ToolGuide and Kyocera's NOVO app provide material-group-specific upper and lower bounds. When in doubt, start conservative — you can always push harder on the second part.
Scenario: Machining 4140 alloy steel (HB 280) on a Mazak VMC, using a Widia solid carbide end mill.
G-code arcs can be programmed with radius (R) or centre-point (I, J) format. The I, J values are the incremental distances from the arc start point to the arc centre. This calculator converts between the two formats.
I, J format is more precise and preferred for CNC programming. R format cannot represent arcs over 180 deg (use IJK or negative R). Some controls handle full circles only with IJK format. For production programs, always use IJK to avoid ambiguity.
Use I, J format: G02 I(radius) J0 F(feed) makes a full clockwise circle. The tool starts and ends at the same point, with I and J defining the centre offset. R format cannot create a full circle because start = end point gives zero radius information.
With R format, use a negative R value for arcs > 180 deg : R-25 means a 25 mm radius arc over 180 deg . Some controls don't support negative R; IJK format is universal. CAM post-processors almost always output IJK format for this reason.
Enter the arc start coordinates (Xs, Ys) and end coordinates (Xe, Ye). The calculator computes the incremental I, J values. For full circle arcs, I = J = 0 and the arc centre is implicit. Verify the arc direction (G02 = CW, G03 = CCW).
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Use the calculator freely. If the result points to a tooling or process problem, we can source the exact carbide tooling you need from vetted factories in China. Compare factory-direct pricing.
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