Why tilt compensation matters on 5-axis machines
When a 5-axis head tilts to reach an angled surface, the tool tip does not stay in the same place unless the control actively compensates for it. Without tool center point management working correctly, or when manually verifying what the control should be doing, the actual tip position shifts in both Z and the lateral plane simply because the tool is now leaning rather than standing straight up.
How the numbers are calculated
Z compensation equals the tool length from the gauge line multiplied by one minus the cosine of the tilt angle from vertical, representing how much the tip effectively retreats in Z as the tool leans over. Lateral compensation equals the tool length multiplied by the sine of the tilt angle, representing how far the tip swings sideways from where it would sit if the tool were still vertical.
Practical tips
This calculation is most useful for sanity-checking that tool center point mode is actually active and behaving correctly, since a control running without TCP compensation will show exactly this kind of position shift on a tilted move. Measure tool length from the same gauge line the control uses internally, since a mismatch there will make the compensation numbers agree with the math but disagree with what the machine actually does.