A drill press and Forstner bit or circle cutter work great for boring holes with diameters exceeding 1". However, if the workpiece doesn't fit on the drill-press table, that approach won't work.

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tech42 template route hole flush trim bit
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A drill press and Forstner bit or circle cutter work great for boring holes with diameters exceeding 1". However, if the workpiece doesn't fit on the drill-press table, that approach won't work.

Locate the center of the hole to be drilled, and with a compass, scribe its circumference on the surface opposite the face side. Next, bore a hole of the desired size in a scrap of 34 "-thick stock. Then, center the hole over the scribed circle and attach it to the workpiece with double-faced tape or clamps as shown. Drill a starter hole large enough to accept a flush- trim bit for your router, and cut the final hole.
—Bruce L. Hasslinger, San Diego