As a private pilot I have long had an interest in aviation. Also, living 20-some miles as the crow flies from a major international airport, it's normal to see airplanes that are in the landing and take off pattern. Sometimes I wonder how high they are. Sometimes, too, I wonder how high the cloud bases are. Is there a rule of thumb for gauging altitude of planes and/or clouds?
Unfortunately there are no rules of thumb for visually estimating altitude. That said, Federal Aviation Regulations can be useful. Over a populated area, or a crowd of people, fixed wing aircraft are required to maintain at least 1,000 feet above the ground unless taking off or landing. Over sparsely populated areas they are to remain at least 500 feet from any person, structure, or vehicle.
There is no minimum altitude requirement over bodies of water. However, I know of one pilot who was trying to see how close he could fly over a frozen lake, lost his depth perception and flew into the ice. After skidding several hundred feet he and his passenger were rescued by ice fishermen on snowmobiles. He was fined and his license suspended for reckless operation.
In general aviation, i.e. small airports, planes generally enter what is known as the downwind leg of their landing pattern. This is the leg that is parallel to the runway on which they are landing and they are headed in the direction opposite to their intended direction of landing. They typically enter this downwind leg at around 1,000 feet.
Small aircraft (and helicopters) when flying on a cross country trip over flat areas usually fly around 4-5,000 feet. This is ignoring the fact that around major airports there are regulations stating how high you can fly at specified distances from the airport.
Flying above 18,000 feet normally requires the aircraft to be on an instrument flight plan (in contact with air traffic controllers), but most small airplanes can't fly that high. Also, one has to be instrument rated and most general aviation pilots of light aircraft are not so rated. Flying above 10,000 feet also requires the plane to have a specific type of transponder. So over flat terrain most small planes are flying way under 10,000 feet.
Direction is also a factor. Generally eastbound traffic (that is flying a compass heading between 1-180 degrees) has to fly at odd 1,000 feet plus 500 feet altitudes: 2,500, 3,500, 4,500, etc. Westbound traffic (181-360 degrees) is to fly at even 1,000 foot plus 500 foot altitude: 4,500, 6,500,8,500 etc.). Instrument flight is at similar altitudes without the 500 foot addition. The reason east-west directions are used instead of north-south is because the magnetic headings can vary a great deal from true north in some areas.
These altitudes are mean sea level, not actual height above the ground.
Above Ground Level - AGL is the altitude expressed in the actual number of feet measured above the ground. If you could take a tape measure and measure from the bottom of your plane to the ground this would be your height above ground level. This requires a radar altimeter, something most general aviation airplanes don't have. Soanother method of determining the proper height to fly above the ground is required...mean sea level.
Mean Sea Level is the elevation of the terrain above sea level. For instance, if the terrain of an airport is 500 feet above sea level, pilots must calibrate their altimeter to read 500 feet while the airplane is sitting on the ground. That way when the altimeter reads 1,500 feet, the plane will actually be 1,000 feet above the ground. Of course MSL level can change, sometimes drastically, and an altimeter setting is also affected by changes in barometric pressure.
As you can see, it's nearly impossible to estimate an airplane's altitude. There are just too many variables. The apparent size of the plane will change with distance and the angle plus you aren't going to know the actual dimensions of the airplane.
However, I did find an interesting site that describes how one can estimate altitude using a digital camera HERE.
Another interesting site is Contrail Science where the author write about contrails and science. It contains a lot if interesting stuff.
This site has a cumulus cloud base calculator that enables you to estimate the height of cumulus clouds at their base.
For more information on clouds visit THIS site.