🧮 Bench tools
The arithmetic of the darkroom, with the sources showing.
Calculators for the numbers film photographers look up at the worst moment: long exposures, warm developer, dilutions, exposure equivalents, filters, bellows, depth of field and pushing. Where a maker publishes the figure, the tool uses the maker's own table and links it.
⏳ Reciprocity: long exposures
Below a certain light level film loses speed, so a long exposure needs more time than the meter says. Each maker publishes its correction its own way: Ilford a formula with a factor per film, Kodak and Foma a table, Fujifilm and Kodak's colour sheets a rule.
1 min 26 s (30^1.31 = 86.1 s, +1⅔ stops)
Source: Harman technology (Ilford), Film reciprocity failure compensation
🌡️ Developing warm or cool
Developer works faster when warm. Ilford's chart converts a time at 20 °C to other temperatures for black-and-white film, rounded to 15 seconds. This reads the chart itself, no formula in between.
5:30 at 24 °C
Source: Harman technology (Ilford), Film development time/temperature compensation chart (April 2002)
⚗️ Dilution
"1+4" means one part concentrate and four parts water: five parts in all. Kodak writes HC-110's dilutions with a colon (B is 1:31), meaning the same thing. Measure the concentrate with a syringe or small graduate; small volumes are where errors creep in.
100 ml concentrate + 400 ml water
Some developers need a minimum amount of concentrate per roll, whatever the dilution: check the maker's sheet before going very dilute. Developers and their dilutions.
☀️ Exposure value and its twins
Every aperture and shutter pair with the same exposure value lets in the same light. Pick one pair; the table gives the others. In bright sun with distinct shadows, Kodak's daylight table for Tri-X 400 gives 1/500 at f/16: the sunny 16 rule.
EV 17 at this setting · EV 15 at ISO 100
| Aperture | f/1.4 | f/2 | f/2.8 | f/4 | f/5.6 | f/8 | f/11 | f/16 | f/22 |
|---|---|---|---|---|---|---|---|---|---|
| Shutter | faster than 1/4000 | faster than 1/4000 | faster than 1/4000 | faster than 1/4000 | 1/4000 s | 1/2000 s | 1/1000 s | 1/500 s | 1/250 s |
EV = log₂(N²/t), the standard definition; shutter speeds rounded to the nearest marked speed. Metering without a screen.
🔴 Filter and bellows factors
A factor is a multiplier on exposure; stops are its base-2 logarithm. A filter factor of 2 is one stop. On a view camera or close up, the lens sits further from the film and the image dims with the square of that distance: the bellows factor.
+1 stop
Use the factor the filter maker prints for your film; it changes with the light and the film's colour sensitivity.
×1.78 +⅔ stops
Factor = (extension ÷ focal length)². At infinity focus the extension equals the focal length and the factor is 1.
📐 Depth of field and hyperfocal distance
How much is acceptably sharp depends on how big the print will be: that is the circle of confusion. The defaults below are common conventions for each format, not a standard; make them smaller if you print large.
2.34 m to 4.19 m · focus at 10.5 m (hyperfocal) and everything from 5.23 m to infinity is acceptably sharp
Thin-lens formulas: H = f²/(N·c) + f; near = s(H − f)/(H + s − 2f); far = s(H − f)/(H − s).
🚀 Push and pull
Rating film above its box speed underexposes it; extra development then raises the highlights, not the shadows. The number of stops is the base-2 logarithm of the ratio. Development times come from the maker's tables, never from this arithmetic.
Push 2 stops
ISO is a measurement, EI is a decision has the makers' push tables for HP5 Plus, Delta 3200 and T-Max P3200.