Convert an arc written with R to its I and J centre offsets, and back. Enter radius, start and end points and the direction — the fix for controls that only accept one format.
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Request a Proposal →There is no difference in the path produced — R and I/J are two ways of telling the control where the arc centre is. The R form gives the radius and lets the control work out the centre; the I/J form gives the centre directly as signed offsets from the arc's start point.
I is the offset in X, J in Y, K in Z (in the G18 and G19 planes). They are offsets to the centre, never to the end point. Sign matters: a negative J means the centre is below the start point.
The trap is the R form's limit. If R is less than half the straight-line distance between the start and end points, the arc is geometrically impossible and the control alarms out. For an arc greater than 180°, R is written negative.
Same start and end point, same radius — the direction word decides which way the arc bows and therefore where the centre lands.
Above 180° the R form needs a negative sign, and some older controls reject it altogether. If the arc is a full circle, or if the geometry is more than a semicircle, use I/J — the centre is unambiguous and cannot be misinterpreted.
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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