Mark the Center of a Rectangular Table
Lay a long straightedge diagonally across the top of the table. Align one side of the straightedge with the two diagonal corners.
Draw a pencil line along the aligned edge, near the center of the table. Move the straightedge to the two opposite diagonal corners and repeat the process. Where the two drawn lines cross is the center of the table.
Remove the straightedge from the table top.
Mark the Center of a Round Table
Place a pencil mark on the outside edge of the round table.
Set a piece of plywood on top of the table. Align one corner of the plywood with the pencil mark.
Hook the end of a tape measure on the plywood corner aligned with the pencil mark you placed on the table. Pull the tape measure along one side of the plywood and note the dimension from the aligned corner to the point the plywood crosses the edge of the table. Repeat the process on the second side of the plywood coming from the aligned corner. Adjust the plywood to make the distance from the corner to the crossing point of the plywood and table top equal. Draw a line along both sides of the plywood with a pencil.
Move the corner of the plywood to one of the two intersection marks. Repeat the process of equaling the length of the two sides of the plywood exiting the corner and marking the intersecting points between the plywood and the sides of the plywood.
Remove the plywood from the round table top.
Align one side of a straightedge with the first two marks you placed on the table top. Draw a line to connect the two points with a pencil. Move the straightedge to the second set of marks and draw a second line. The point the two lines intersect represents the center of the round table.
Drill the Patio Umbrella Hole
Secure a 1-1/2-inch hole saw into the chuck of a 1/2-inch drill motor.
Align the drill bit of the hole saw with the intersecting marks designating the center of the table.
Drill through the table top. Keep the drill motor perpendicular to the table top to ensure you drill the hole straight through the table top.
Secure the 1-1/2-inch spade bit in the chuck of the drill motor.
Measure the length of the spreader located between the bottom legs of the table. Depending on the design of the table, your table may not have a spreader.
Divide the spreader measurement in half. Mark the divided distance on the top of the spreader with a pencil. Mark half the width of the spreader to mark the center of the spreader.
Drill a 1-1/2-inch hole through the spreader with the spade bit. Make sure the center of the spade bit aligns with the spreader center marks.
Remove rough edges by sanding around both 1-1/2-inch holes with 80-grit sandpaper.
Slide the patio umbrella pole into the drilled holes.