An aspiring chef was taking about some of the rules of thumb she is learning
° to tear Saran Wrap, put your thumb on the W of the box
° for potato salad use one and a half medium potatoes and an egg per person
° good popcorn pops to 33 cups for every cup of seeds
° use a third the amount of a dried herb to replace its fresh version
° food cost is usually about 25% to 30% of sales
° drive through sales are 40% to 50% of a fast food restaurant's business
° hamburger should be cooked to at least 155° F
° for catering you should have a half pound of uncooked meat and three quarters of a pound of side dishes per person
° leave the oven door cracked open when broiling in an electric oven, closed when using gas
I mentioned a calendar trick and, without effort, dozens come to mind:
° In any calendar year 4/4, 6/6, 8/8, 10/10 and 12/12 will fall on the same weekday - Wednesday for 2012...
° An average adult of normal weight requires about 100 watts of power from food
° skeletal muscle is about 20% efficient
° a car with an internal combustion engine radiates about three quarters of the energy in the gasoline it burns as waste heat
° a person on a bicycle is about three times as efficient as someone who is just walking
° the average adult male in good physical shape should be able to provide a kilowatt-hour of physical work in a day.
° the average home uses about one kilowatt of power
° the average nuclear power plant generates about a billion watts of power - so it can run the homes in a city with a million residents (San Diego is very close to this)
° electric motors are about 90% efficient
° a pound of fat is equivalent to about 3,500 Calories
° fat, pound for pound, has a similar amount of energy as gasoline
° losing more than three percent of your weight per month in a diet is medically dangerous
° fewer than five percent of dieters are at or below their starting weight two years later (the surest way to gain weight is to go on a diet)
° there are about Pi * 107 seconds in a year and about 8,800 hours in a year
° it takes about an acre of land to feed a person
° getting your energy from beef requires about ten times as much plant energy as just eating the plants
° about 1000 watts of solar power per meter makes it to the ground with the Sun directly overheat on a perfectly clear day
° molecules in an ideal gas at room temperature have an average kinetic energy of about 1/40th of an electron volt.
° digital music needs to be sampled at least at twice its highest frequency
° when estimating angular widths stretch your arm out: your finger tip is about 1°; the distance across your index, middle and ring fingers is about 5°; your fist 10°; the space between your outstretched pinky and index finger 15°, and the span between your outstretched thumb and index finger is about 25°
° the angular size of the sun and moon are both about a half degree
Any field will have rules of thumb for quickly making approximations with very little work. You can probably list a few dozen with five minutes of reflection (if you have some interesting ones add them as comments).
The etymology of the term is hazy, but the sources I've seen either relate it to an approximation for length based on the thumb (inch and thumb are commonly linked in European languages) or for some agricultural purpose like the depth for planting seeds.
I find it useful to make many back of the envelope calculations as I come to grips with a problem. There are a lot of tricks - units analysis (which tells you mc2 has the units of energy, mc3 or mc don't. Many calculations are speeded along with drawings for visualization and approximations for doing mental or back of the envelope math. I'm a big fan of slide rules. Learning to use one gives you a natural sense of what a logarithm is. You had to know roughly what the answer might be and keep track of the order of magnitude in your head. I was banned from using mine when invited to some corporate strategy sessions at a big telecom that I used to work for -- I was out-calculating the guys who were using laptops (they often got their answers wrong to 8 significant decimal places) and it was somehow wrong to have a researcher doing that... I recommend learning how to use one if you want a more intimate relationship with back of the envelop calculations.
There is probably a lot of information about any field embedded in its rules of thumb and how they change with time.