Quick-Reckoning Hyperfocal Distance ...


A recent thread at mu-43 asking about hyperfocal distance and maximising depth-of-field led to an interesting post by one of the locals , giving details of an aide-memoire system for hyperfocal distances that I hadn't come across before.

There are other ways of doing this, of course, such as carrying or memorising DOF tables (Google for DOFMaster), or using smartphone apps (whatever they might be)

Asking one of our esteemed moderators if it were possible to copy the thread across, I was told not, but it was suggested I might write something myself (yeah, thanks, bruv ...)

I'm not going to go into the ins-and-outs of hyperfocal distance and optical equations, because we can Google for that, or even read about it in a book (a paper one I mean), plus I'm certainly not qualified ... so “What is hyperfocal distance and why should I care what it is?” is a subject for another thread.


The gist of the idea is that, by remembering a few simple numbers and being able to perform some basic mental arithmetic, we can rapidly work out what the hyperfocal distance is for any lens focal length and f/stop combination.

I latched onto this because 1) my memory is a bit shot 2) I can't memorise all the hyperfocal distances for the few manual primes I use at all the f/stops and 3) I'm a bit of a sad sack

So ... it works like this:

For each focal length lens you use, there is a “K” number associated with it. (“K” is a conventional notation, it has no intrinsic meaning). The “K” number changes between camera formats, by the way, so the “K” number for a lens on a micro4/3 camera will be different from the “K” number of a lens with the same focal length, but used on a camera with a different sized sensor, such as APS-C or “full-frame”.

We can use this “K” number as the basis for doing a quick sum to establish hyperfocal distance in the field (or, indeed, the street), so long as we also know what f/stop we're using. As there's one “K” number per lens, it's a bit easier to memorise than a set of DOF tables. Probably.

As I'm a micro4/3 user, I'll work in micro4/3 numbers ... I'll explain about different sensor sizes later ... and let's forget zooms. And let's forget engraved DOF scales (because then all you have to do is set the infinity mark at twice the f/stop you're using and Robert's your Father's brother)

(continued in next post)


Ok ... now what?

Well, let's say I'm wandering about town with my lovely, but manual, Voigtlander 28mm. I'm on the move and so is everything else. I'm seeing plenty to snap, but I don't have time or inclination to refocus for each shot. I want as much of each scene I shoot “acceptably sharp” -- good enough for jazz, as they say. It's bright enough for f/8, and I'm going to let the camera sort out the shutter speed.

But where do I focus to get this? I know that I've got a 28mm lens – and I know the associated “K” number (50). I know what f/stop I'm using (8). So what I need to do is do divide the K-number by the f/stop – in this case 50/8, which is 6.25.

So what I do now is focus on an object 6.25 metres away, and leave the lens there. Every shot from now (assuming I don't move the focus ring or f/stop) will be in focus from approximately 3m to infinity.

Similarly, using the 28mm at f/4, I'd need to focus on an object ~13m away (because 50/4=12.5)

On micro4/3, these are some “common” focal lengths and their “K” numbers:

(mm) K-no.

14 -- 13
17 -- 20
20 -- 28
25 -- 42
28 -- 50
50 -- 160

(These are heavily rounded to make the sums easier :) - small errors are really going to make very little difference “in the field”)

Similarly again, if I have the Lumix 20mm on, and it's an f/8 sort of day, then 3.5m is the focus point. This starts to break down if you have poor mental arithmetic skills and it's an f/5.6 sort of day, of course ...

(continued in next post)


Where does the “K” number come from?

The “K” number for any focal length on a 4/3 sensor is calculated using the formula:

f² / 15 (where f = focal length in mm),

Why 15? The short answer is, that's the “Circle of Confusion” (CoC) for a 4/3 sensor in 1000ths of a metre ... which is why all the sums above lead to answers in metres. Now you're going to ask (if you don't already know) “What's the Circle of Confusion?” ... and I'm going to say, Google Is Your Friend. Because it will find you a nice Wikipedia article all about it ...

More generally,
f² / c (where f = focal length in mm, and c = Circle of Confusion in mm),

Just so's you know, the CoC for a full frame sensor is 30, and for a Sony APS-C is 20.

Now you can work out all the K numbers for your own lenses ... and for those who like feet rather than metres ... um ... multiply by 3.3 or something; I haven't found a reliable source of CoC in feet yet ...

Anyway, I hope this has been clear enough and useful enough to be of help to at least one person ... if not, you are very welcome to post corrections and clarifications ...