Neutral Density Filter Stop Calculator

A neutral density filter attenuates all visible wavelengths by roughly the same amount, so it buys exposure time without shifting the colour balance of the scene. Its strength is described three interchangeable ways. Optical density D is the base-10 logarithm of opacity, so D equals log10 of 1 divided by transmittance. Stops are D divided by log10 of 2, about 0.301, and the filter factor is simply 2 raised to the number of stops. An ND 0.3 passes 50 percent of the light and costs 1 stop, ND 0.9 passes 12.5 percent for 3 stops, and ND 3.0 passes about 0.098 percent for 10 stops. Because every stop doubles the required exposure time, the new shutter duration is the metered duration multiplied by the filter factor: a metered 1/250 second behind a 6-stop filter, factor 64, becomes about 0.256 second. Labelling is the usual source of error, since one maker prints ND8 meaning a factor of 8, another prints 0.9 meaning the density, and a third prints ND1000 for the same 10-stop glass. Several practical caveats limit the arithmetic. Strong filters are rarely perfectly neutral, and 10-stop resin or glass commonly leaves a blue or magenta cast that has to be corrected in white balance or raw processing. Many ND coatings attenuate visible light far more than near-infrared, so long daylight exposures on digital sensors can show infrared pollution as a reddish-brown wash, most visible in foliage. Through-the-lens metering becomes unreliable past roughly 6 stops because too little light reaches the meter, so the standard workflow is to meter and focus first, then attach the filter and apply the calculated factor. Variable filters built from two crossed polarisers follow Malus law and typically develop an uneven X-shaped darkening beyond about 6 stops. Stacking filters adds stops cleanly but also stacks vignetting and reflections, which is a real constraint on lenses wider than about 24mm. Reciprocity failure lengthens exposures further on film but does not apply to digital sensors.

The density notation used on ND filters comes from photographic sensitometry rather than from optics manufacturing. Ferdinand Hurter and Vero Driffield, working in Widnes in England, published their foundational study of photographic densities and characteristic curves in 1890 through the Society of Chemical Industry, establishing density as the logarithm of opacity, the convention that still gives a 10-stop filter its 3.0 label. Commercial neutral density material followed the growth of the gelatin filter trade. Frederick Wratten founded Wratten and Wainwright in London in 1878 and the firm became the main supplier of dyed gelatin filters; Kodak acquired it in 1912 and continued the Wratten numbering, in which the neutral density series carried the number 96 with the density printed alongside. Use of the filters was driven first by motion picture work, where cinematographers needed to hold a wide aperture and a fixed shutter angle under daylight or arc lighting, and only later became a landscape staple. The graduated version, dark at the top and clear at the bottom, was developed to hold back bright skies on film stocks with limited latitude. Daytime long exposure as a mainstream still technique is much more recent and follows the arrival of dedicated 10-stop products, with Lee Filters and its Big Stopper joined by comparable glass from Hoya, B and W, NiSi and Haida. The variable filter, meanwhile, applies a much older piece of physics: Etienne-Louis Malus described in 1809 how transmission through crossed polarisers varies with the square of the cosine of the angle between them, which is exactly the mechanism a rotating variable ND exploits.