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Cutting Parameters

Arc R to IJ Centre Point Converter

TiAlN coating benefits for carbide tools. Get instant I (mm), J (mm), Arc Center X,Y for your machining parameters.

Input Parameters

Results

I (mm)
J (mm)
Arc Center X,Y
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The Engineering Behind Arc R to IJ Converter

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.

Engineering Note

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.

Worked Example: Step-by-Step

Scenario: Machining 4140 alloy steel (HB 280) on a Mazak VMC, using a Widia solid carbide end mill.

Step 1 — Gather inputsDiameter 12mm, SFM 180 Step 2 — Compute RPMRPM = (180 × 1000) / (π × 12) ≈ 4,775 Step 3 — Apply to the formulaFeed = 4,775 × 4 × 0.05 = 955 mm/min Step 4 — VerifyChip load 0.05 mm/tooth ✓

Arc centre point I J conversion formulas

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.

Frequently asked questions

R format vs IJ format -- which is better?

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.

How do I program a full circle with G02/G03?

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.

What if my arc is over 180 deg ?

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.

How to use this Arc R to IJ Centre Point Converter

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).

Common mistakes to avoid

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