View Full Version : math question re: enlarging

16-Sep-2003, 10:55
Hello all:

The recent post regarding math made me wonder if there is a handy formula for determining what adjustment in time is required when moving from one enlarger height to another.

For example, if I have made a good work print at an enlarger height of 7.5 inches (as indicated on the enlarger column)with an exposure of 9 seconds at f 11, what increase in time would be necessary to produce an identical exposure if the enlarger height is increased to 12 inches?

Thus far I've been doing this via test strips, but I'd like to learn a more efficient method.


Sidney Cammeresi
16-Sep-2003, 11:26
oh = original height, nh = new height, oe = original exposure, ne = new exposure

ne = oe * (nh / oh)^2

If you increase the height by a factor of n, then each dimension increases by a factor of n, so the area increases by a factor of n^2, and exposure is proportional to area. (This ignores any reciprocity issues, of course.)

Andrew O'Neill
16-Sep-2003, 11:40
Yep! Works for me too: original time X new lens to paper distance squared, divided by the old lens to paper distance squared. This will give you your new exposure time but I must also add that it'll get the puck crease, not in the net. You may have to adjust time slightly and contrast as well. I always take this new time and make a test strip around it. Have fun, eh!

Andrew O'Neill
16-Sep-2003, 11:41
er....that should read "get the puck in the crease"...sorry, lacing up for hockey season.

Dave Schneider
16-Sep-2003, 13:44
That formula will get you in the ballpark. It is much more precise though to calculate based on the magnification. Exposure time B = ((MagB+1/MagA+1)^2)* exposure time A. Magnification is easy to determine with the height from the easel to the optical center of the lens. I have a spreadsheet running on my palm computer that works great for this.

Matthew Hoag
16-Sep-2003, 17:17
Ignoring the math, if you have a light meter you can take a reading at your original height then take another at your next column height. Take the reading difference on your meter and adjust your enlarging lens aperature until the second meter reading is equal to the first or change the f-stops into a time adjustment. Before I went to contact printing this worked well for me.



Scott Soper
16-Sep-2003, 18:34
The above formulas will indeed get you in the ballpark, but don't forget to include bellows factor. If you start with a 2x enlargement, then raise the enlarger for a 4x enlargement, your effective f stop changes when you refocus (just like when you're shooting closeups with the camera).

Dave Schneider
16-Sep-2003, 21:09
Scott, You're going to have to clear that up for me. If we use a formula that calculates the difference in magnification factors, or a simpler formula that only includes image size, where does another 'bellows' factor come into play? The bellows factor we use in correcting exposures with the camera at closer focus distances is based on magnification, not magnification and another bellows factor. Please clarify what I'm missing?

Doremus Scudder
17-Sep-2003, 01:51
Hello all,

I have a (rather ancient) Kodak B&W Darkroom Dataguide with a nifty little calculating wheel for precisely this purpose (slide rule style). It calculates using differences in one dimension of the print as related to exposure time. One sets the current exposure time opposite a side length of the original print and then simply reads the new exposure opposite the desired new dimension.

This seems to be based upon a formula using magnification similar to that which Dave mentioned earlier. Any of you math wizards able to come up with a simple formula that includes only exposure times and one dimension of the print? This would seem the most workable solution for those without a calculating wheel...

TIA ;^D)

Scott Soper
17-Sep-2003, 18:55

I haven't used your formula, but it looks pretty good. I have a recent Kodak B&W Dataguide (not with me, unfortunately), and the enlargement wheel indicates something like what you've posted, I believe. I was looking more at Sidney's formula, which doesn't take bellows factor into account.

Guess I shouldn't have opened my big mouth!

BTW, Matthew's suggestion about the light meter works great, IMHO.