Your Routed Corners Are Round

Two ways to make a rectangular hole, with opposite constraints

You have drawn a 2.0 x 1.0 mm opening. The fabricator can drill it or rout it, and the two paths constrain you in opposite directions.

Drilling means finding a round hole that fully contains the rectangle. A circle contains a rectangle only if its diameter reaches corner to corner, so the requirement is the Pythagorean diagonal:

sqrt(2.0^2 + 1.0^2) = 2.2361 mm

Routing reverses it. The cutter has to fit inside the opening, so it is bounded by the short side — 1.0 mm here — and you want the largest tool that fits, not the smallest that covers.

Same rectangle. One constraint says "at least 2.2361", the other says "at most 1.0". Neither is a rounding of the other.

Round up, never down

Tooling is stocked on a grid. Board shops hold metric drills in 0.05 mm steps, so 2.2361 mm is not a size anybody has. The next one up is 2.25 mm, which is 0.0139 mm larger than you strictly need.

That oversize is the price of a stocked grid, and it is not negotiable. What matters is the direction: rounding down to 2.20 mm leaves the corners of your rectangle uncut. That is not a small error and a slightly-too-small hole — it is a hole that does not do the job it was drawn for.

If you specify an exact decimal that falls between stocked sizes, the shop will quote the next size up. You may as well know which one that is and put it on the drawing yourself, so the choice is documented rather than made for you in CAM.

Your routed corners will not be square

This one surprises people every time, and it is pure geometry: a router cuts with a round tool, so every internal corner comes back with a radius of exactly half the cutter diameter.

For the 2.0 x 1.0 mm opening, the largest stocked cutter that fits the 1.0 mm short side is 1.0 mm, leaving a 0.5 mm corner radius. That is half the short side. What arrives is not a rectangle with slightly soft corners — it is an obround, a slot with fully rounded ends, and no amount of CAM programming changes it.

When the corner radius climbs past about a quarter of the short side, stop drawing a rectangle and draw the obround you are actually going to get. The clearance check then uses the real shape instead of an optimistic one.

If a genuinely square corner is functionally required, the opening has to be made another way — a corner relief, a secondary operation, or a different feature entirely. It is not something to specify harder and hope for.

When the answer is "you cannot"

Both directions have limits, and they are real answers rather than failures to compute one.

Ask for a hole larger than the biggest stocked drill and the opening is a routed feature, not a drilled one. Ask to rout a slot narrower than the smallest stocked cutter and it cannot be routed at all. A calculator that responds by naming a tool nobody stocks has told you something worse than nothing.

Why the metric conversions are exact

One small thing worth knowing when you read a drill chart: the inch-to-millimetre figures in it are not measurements. Since the international yard and pound agreement of 1959, one inch is defined as 25.4 mm exactly. A number 1 drill is 0.2280 in and therefore 5.7912 mm, with no rounding anywhere in that step.

What is not exact is the tool inventory. Number drills, letter drills and fractional sizes are historical series that happen to exist; the metric 0.05 mm grid is what a board shop actually stocks. Converting between them is arithmetic, but availability is a question for your fabricator.

The cheap answer is often the right one

For small openings, a single drill hit costs far less than a routed slot. If the part clears the round hole, the shape of the hole does not matter — and the diagonal tells you the smallest round hole that contains the rectangle you drew.

It is worth checking that before specifying a rout. Plenty of rectangular apertures on plenty of boards exist because someone drew a rectangle, not because anything needed one.