Calculate exposure time in the darkroom for different enlarger heights

When you do your own printing as a photographer in the darkroom, you have to make a lot of testprints to determine the correct exposure. The problem is that wasting paper on teststrips is expensive.

One way to save on paper costs is to make your teststrips and test exposure on a small image format and then scale up the image once you are happy with how your print looks.

There are 3 ways to scale up your image:

• make new teststrips to match the previously found exposure (which is wasting paper again)
• use a lightmeter to find the difference in light output between the new and the old height of your enlarger
• calculate the new exposure times

I opted to make the calculation by using some simple trigonometry. Maybe others can benefit from this as well. If you don't want to mess with the formula, you can use this online spreadsheet to mark your own exposure compensation f-stop setting on your enlarger column.

Here are the instructions:

Turn the enlarger all the way up and insert the negative carrier without a negative. Focus on a piece of paper under your enlarger. Now measure the longest side of the projected image on the paper and note this value as "y".

Then turn the enlarger all the way down (or: the lowest level you might ever want to use), focus and mark this point (or write it down if your enlarger has a measurement scale on the column). Measure the the longest side of the negative carrier mask on the paper again (ie. the width of the projected image)  and note this value as "x"

You now have two marks on your enlarger column. Measure the difference in height between the lowest and highest mark and note this value as "c".

Now we are going to calculate the light output for the differences in enlarger height in f-stops, starting from the highest position (=lowest light output) as reference value "1".

To find the F-stop value for a given height "h" (in centimeters above the minimum height) use the following formula:

f-stop= (y / (x+ h/c * (y-x)))ˆ2 

(or, use the online spreadsheet)

Here's an example of how to use this:

My values measured c=100cm, y=50cm and x=5cm.

When I make my teststrips at a column height of 25cm above the lower mark and I want to make my final print at the maximum hight (to make a 50cm wide print), I need to multiply my found exposure time with 9.47.