I read everyone's answer and did some of my own research to find an estimation method that satisfies me and might be helpful to others too. I think it should be roughly ±20% accurate.
For any amount of "good strength" American-style coffee by any brew method, weigh the dry coffee in grams and multiply by 0.008, or 80mg of caffeine for each 10g of dry coffee.
Weakly extracted coffee might yield 0.6% of its weight in caffeine and very strongly extracted coffee might get close to 1% caffeine.
These numbers are for typical 100% Arabica or mostly Arabica blends. 100% Robusta beans (uncommon) could be about double the caffeine.
Maximum caffeine content
Typical premium roasted Arabica coffee beans like mine contain close to 1% caffeine by mass when measured by spectrophotometer (p 311)
though Robusta (less common and usually blended with Arabica in cheaper coffees) has
roughly twice that
If you have a health concern like wanting to stay under the 300 mg guideline for pregnant women, you should be able to use this as the upper limit: each 10g of Arabica coffee contains about 100mg of caffeine.
I use a 2 Tbsp scoop to measure beans before I grind them. One scoop of
beans weighs about 12 grams (yes I tared the scoop, but I did only weigh
once and am not comparing light or dark roasts which will vary in weight
So if I eat that scoop of beans or grind them finely and drink them
with any amount of water I will be consuming the 120 mg (1% of 12g) of caffeine
present in them. That should be an upper limit to this estimation
exercise. The strongest or biggest/weakest cup of coffee I can brew with
that scoop of beans will have no more than 120mg caffeine.
How strong is my cup?
Typical American-style brewing methods and water ratios result in
1% (weak) to 1.65% (too strong) disolved coffee solids, with 1.25%
considered optimal whereas
"a typical espresso will contain on average 1.8-2.2%"
So 1 fl oz of brewed coffee or espresso weighs almost the same as water
(29.57 g) and contains 1-2% coffee solids (so about 300-600mg, or 380mg solids for optimal brewed coffee and 600mg solids for espresso). That would be the upper limit if the coffee solids were pure caffeine, but they can't be.
On the other hand,the caffeine is probably more soluble than the other parts of the bean,so even though it's only 1% of the mass of the beans it's probably more than 1% of the dissolved solids. That's the hard part. Coffeechemistry.com says brewed coffee ends up with 8-15 mg caffeine per oz and espresso 30-50 mg caffeine per oz. That's a pretty huge range. It means caffeine is 2.5-4.0% of the solids (380 mg) in an ounce of "optimal" brewed coffee or 5.0-8.3% of the solids (600 mg) in an ounce of espresso.
So: I typically make a nice strong 10 oz cup of coffee with my 12g of
beans containing a maximum of 120mg (or 1% of the coffee mass) caffeine. So let's say this maximum 12 mg caffeine per each oz of coffee corresponds to 1.65% or 500 mg solids (1.65% of 29.57 gr = 500 mg). In this case the 12 mg caffeine is 2.4% of the solids. If I brew it "too weak" and it ends up 1% solids (or 300 mg per oz) I would guess I'd proportionally get no more than 60% of the max caffeine, 7.2 mg (again 2.4% of the solids) per oz or 72 mg for a 10oz cup. So that narrows the range to 72-120 mg of caffeine in my cup depending on the brew strength.
I'm guessing a good cup ends up somewhere in the middle, so I'm going to estimate my typical cup contains around 100 mg of caffeine from its 12g dry coffee, or about 80% of the maximum caffeine present in the beans. From this I would suggest a decent rule of thumb for "optimal" strength American-style brewed coffee is around 0.8% (or 0.008) of the mass of the beans used, or 80mg of caffeine for each 10g of dry coffee.
Bonus corollary/sanity check
Using the same method, a shot of espresso made with 7g of ground
coffee maxes out around 70mg caffeine (77mg if 10% Robusta sometimes typical for Espresso blends), but the serving size and strength are more standardized than brewed coffee, so the 64mg/shot reported by the USDA and others also ends up being 80-90% of the caffeine present in the beans.