Neutral density filter calculator
ND filters are labelled three different ways — stops, optical density and factor — and the three get confused constantly.
1/x seconds
stops
Exposure with the filter
0:00:08.2
- In minutes
- 0.137
- Filter factor
- 1024
- Optical density
- 3.010
- Light transmitted
- 0.097 66 %
- Total stops
- 10.00
Show the working
- Shutter speed without the filter = 125
- Filter strength = 10
- Extra stops from a second filter = 0
- base_seconds = 1 / 125 = 0.008
- Total stops = 10 + 0 = 10
- Filter factor = 2^10 = 1024
- Exposure with the filter = 0.008 * 1024 = 8.192
- Optical density = 10 * 0.30102999566398 = 3.0103
- Light transmitted = 100 / 1024 = 0.097 656 3
- In minutes = 8.192 / 60 = 0.136 533
Values are shown to six significant figures here; the arithmetic itself runs on exact fractions and is only rounded where a number is printed.
Scenarios & local history
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The formula
- new exposure = base exposure x 2^stops
- optical density = stops x log10(2) = stops x 0.30103
- an ND1000 is 10 stops, density 3.0, transmitting 0.1% of the light
Very long exposures also suffer reciprocity failure on film and heat noise on digital, both of which push the real time longer.