Section 107.51 sets three operating limits that show up together: groundspeed, altitude, and weather. The weather pair is visibility and distance from clouds. They are statute miles and feet, measured from specific places. The test swaps the units and the places.
Visibility
Flight visibility must be no less than 3 statute miles. The regulation defines flight visibility as the average slant distance from the control station at which prominent unlighted objects can be seen and identified by day, and prominent lighted objects by night. The observation point is the control station. It is not the camera on the aircraft, it is not a guess from the aircraft's position, and it is not automatically the automated weather station a few miles away. A METAR is a tool for the preflight in §107.49. If it says 2SM, you already have a problem. If it says 10SM and you are standing in a fog bank, you still do not have 3 statute miles at the control station.
Three nautical miles is longer than 3 statute miles and is the wrong unit. One statute mile and 5 statute miles are different minimums. Basic VFR cloud clearances for manned aircraft in some airspace classes are not the Part 107 numbers.
Section 107.51(c) places the visibility observation at the control station. Section 107.51(d) places the cloud distances on the aircraft: 500 feet below, and 2,000 feet horizontally. Both limits apply in Class G. Controlled airspace does not replace them with a different cloud table, and a LAANC authorization does not waive them. If you need to fly closer to a cloud than those distances, that is a waiver of §107.51, not a chart interpretation.
Clouds
The aircraft must remain at least 500 feet below the cloud and 2,000 feet horizontally from the cloud. Memorize them in that order so you do not swap them. A plan to fly 300 feet below a cloud base fails even if you are 2,500 feet horizontally from the cloud bank. The vertical minimum is 500 feet, not 300. The two distances are not added together, and there is no "1 statute mile from clouds" rule in §107.51.
There is no "above the cloud" distance because a small unmanned aircraft may not be operated above a cloud. AC 107-2A, as the course teaches this point, also says there cannot be a cloud or similar obstruction between the aircraft and the remote pilot. That connects the cloud rule to visual line of sight. If a cloud sits between you and the aircraft, you cannot see it, and you are not 500 feet below the cloud either.
Putting the numbers in a ceiling
Over open terrain with a solid deck at 1,200 feet AGL, 500 feet below the base would be 700 feet AGL. The 400-foot rule is lower, so the highest legal altitude is 400 feet AGL. If the deck is at 600 feet AGL, 500 feet below it is 100 feet AGL, and that lower number controls. Always take the more restrictive limit.
A scattered layer is not automatically a ceiling in a METAR, but any cloud you would enter or fly above is still a §107.51 problem. Decode the METAR on the METAR page, then apply these distances to the layer that is actually there.
Haze, smoke, and fog are the weather that drops visibility under 3 statute miles without a dramatic ceiling. They are a no-go for the same reason a 2SM METAR is a no-go. Anti-collision lights at night do not reduce the 3-statute-mile requirement. Night adds a light. It does not subtract a mile.