Why arc length and chord length matter in CNC work
Arc moves show up constantly in CNC programming, from G02 and G03 circular interpolation to laying out radiused pockets and fillets, and two different numbers matter for different reasons. Arc length tells you how far the cutter actually travels along the curve, which feeds into cycle time and feed rate math. Chord length tells you the straight-line distance between the start and end points, which is what you would measure with calipers to check the part.
How the numbers are calculated
Arc length equals the radius multiplied by the arc angle, with the angle converted to radians first. Chord length equals two times the radius multiplied by the sine of half the arc angle. For a small arc angle the two numbers stay close together, but as the angle approaches a full half circle the chord length levels off toward the diameter while the arc length keeps growing.
Practical tips
Use arc length when estimating cycle time for an arc move at a given feed rate, since that is the actual path the tool travels. Use chord length when checking a finished part against a drawing with calipers or a height gauge, since that is the dimension you can physically measure without tracing the curve.