I can use a DoF calculator, or crunch the heavy math by hand if I really want to know exactly what my DoF is going to be... but most of the time knowing exactly is actually overkill, and taking the time to pull out a DoF calculator is impractical. I'm wondering if anyone knows of a 'rule of thumb' that is common for quickly figuring out a rough estimate of what my DoF will be when I'm in the field...
Depth of field formulas are indeed complex and nonlinear, but they still afford useful rules of thumb. For medium subject distances (not too close to the lens, compared to its focal length, and not so far away that the DoF extends to infinity), the DoF is approximately proportional to:
The square of the distance.
The inverse square of the lens's focal length.
This assumes a given standard of blurriness (usually quantified as the diameter of the circle of confusion), which depends on your sensor, intended magnification of the ultimate images, your visual acuity, and many other things. For this reason I'm not going to recommend one rule for everyone, but rather will explain how to develop your own rule(s) for your own purposes.
To make this aproximation work, you only need to know the DoF for a standard f-stop, a standard distance, and a standard lens, chosen in advance by you. For instance, let's set the diameter of the circle of confusion to 0.02 mm (a fairly small size, but not uncommon). Then, using an online DoF calculator, we obtain a depth of field of 1.59 m = 5.2 feet for a subject at 10 meters from a 100 mm lens at f/4. Using only these data (10m, 100mm, f/4, 5.2 ft), we can now anticipate the DoF for any similar exposure combination by making a series of simple adjustments. For example,
Doubling the f-stop from f/4 to f/8 should double the DoF from 5.2 to 10.4 feet. (Actual value: 10.66 feet.) Halving the f-stop from f/4 to f/2 should halve the DoF from 5.2 to 2.6 feet. (Actual value: 2.59 feet.)
Now, continuing from f/2, halving the subject distance to 5 meters should divide the DoF by four, giving 2.6/4 = 0.65 feet. (Actual value: 0.66 feet.)
Halving the lens's focal length from 100 mm to 50 mm should quadruple the DoF. Continuing from the previous result, it should go from 0.65 ft back to 2.6 feet. (Actual value: 2.62 feet.)
In this example we have worked out the DoF at 5 meters for a 50 mm lens at f/2 using simple multiplications and divisions and we have made only an inconsequential error of less than 1% in our estimate.
Thus, if you choose a standard combination of focal length, f-stop, and subject distance close to those about which you are usually concerned, you need only memorize a single DoF value which you can rescale as appropriate in the field.
Typically, you might work out the DoF for a trial shot and then use this rule of thumb to anticipate the effects of proposed changes (of distance to subject, aperture, and even choice of lens) on the DoF. This needn't even involve a calculation. For example, after examining an initial shot closely, you might decide you need twice the depth of field (even though you don't know exactly, as a number, what the current DoF really is). Your options therefore include:
Double the f-stop. (Watch out, though, for diffraction blurring once the aperture gets smaller than a few millimeters!)
Move back from the subject to increase its distance to the lens by about 40% (1.4^2 = 2 more or less).
Use a lens of about 0.7 times the focal length (0.7^2 = 1/2 more or less). E.g., change from a 50 mm to a 35 mm lens.
Although the first option is so quick you might forgo any calculation and just try it, the next two could be sufficiently cumbersome or time-consuming that having this rule of thumb might just be useful ;-).
Note that the approximation breaks down for macro photography and landscape photography. In both cases one usually has more time to prepare and test shots so perhaps having a quick rule of thumb is less important in those situations.
Depending on the brand and type of lens, it may be right on the lens itself -- there may be a set of lines between the aperture ring and the focus ring/focal distance indicator that will give you an indication of the "acceptable" circle of confusion range at various f-stops (usually at two-stop intervals). (It's sometimes called the hyperfocal distance indicator -- set the infinity mark at or within the range of the far-distance bracket, and everything should be more-or-less in focus from infinity to the distance indicated at the near-focus bracket for that f-stop.) If you are after a max DoF, there's good evidence supporting a strategy based on focusing at infinity and allowing the size of the aperture to determine the minimum resolved object size. F'rinstance, a 35mm lens set to f/22 and focused at infinity will adequately resolve objects to a resolution of (35/22=) 1.6mm. (See The Ins and Outs of Focus for details.)
There's no simple rule of thumb due to the inhearent nonlinearity in the equations.
The DOF marks on lenses are in my opinion a waste of time. First off they are based on an approximate formula that doesn't take into account the asymettric nature of dpeth of field (at close distances the DOF extends further infront of the subject and at larger distances it extends further behind). Secondly the distance scale is highly nonlinear and marked infrequently so you have to guess the distance which corresponds to the mark.
So once you've guessed the distances you want in focus, and guessed what distances the DOF marks actually correspond to, and fed the guesses into an approximation, what you get back probably isn't a lot of use.
With most things such as exposure I would also recommend avoiding rules of thumb and just shoot, eventually you will get a feel and be able to regularly get it close first time.
DOF is more complicated and in some cases downright deceptive. You will develop a rough idea but that's not usually good enough. Even now, if I'm concerned about focus I will check and reshoot. Every time.
Shoot an image review it and look at what is in focus and what isn't. Why settle for guesses and approximations, when you can have the actual answer in front of you in seconds!
Canon users who have installed Magic Lantern on their cameras can enable a depth of field display as described in the Magic Lantern user guide. The display includes the near and far distance from the point of focus.
I don't think there is just a general rule of thumb because of the number of variables such as aperture, focal length, circle of confusion, etc. If the lens, itself, has DoF markings, that's great, but many do not. So, one option, is to do the basic calculations ahead of time for your favourite lenses and put them on a cheat sheet, maybe an index card for each lens, and then quickly refer to it as you need. If you have a few seconds to do a simple calculation, then you probably have enough time to do a quick reference if the appropriate card is kept handy. Heck, doing that may show a pattern for each lens that you can use to derive your own simple formula.
One of the things that finally "clicked" with me and DOF is to think of DOF as dependent on magnification -- not distance or focal length.
For example, 20' at 100mm has the same DOF as 10' at 200mm. Think about macro: Distance doesn't change the DOF -- the degree of magnification of the subject on the sensor does.
What this does for me is I think about the size of the person in the frame and mostly ignore the focal length in my f-stop estimates. I intuitively know what DOF I'll get from a headshot vs a full body shot at f2.8 -- and that is independent of distance or focal length.
I know the backgrounds will be significantly different between long and short, but I can see that easily in the view finder.