Why ND8 and ND64 Stacked Make ND512

This page contains affiliate links. If you buy through one we may earn a commission, at no cost to you.

Yes, four stops and six stops stacked give you ten stops, and stops are the only notation on a filter that you are allowed to add. The trap is that most filters are not labelled in stops. They are labelled with the factor, and factors multiply. An ND8 stacked on an ND64 is not an ND72. It is an ND512, and that is nine stops, and nine stops is the difference between water you have frozen and water you have smoothed.

A stop is one halving or one doubling of the light reaching the sensor. That is the entire definition, and everything else in exposure follows from it.

One quantity, three ways of printing it

An ND filter's job is to pass a known fraction of the light. The fraction can be written three ways and all three are in use.

The factor is the reciprocal of the transmission. An ND8 passes one eighth, which is 2 to the power of minus 3, which is 3 stops. An ND64 passes one sixty fourth, which is 2 to the power of minus 6, which is 6 stops. So the factors you see on rings are powers of two, and the exponent is the stop count. ND2 is 1 stop, ND4 is 2, ND8 is 3, ND16 is 4, ND32 is 5, ND64 is 6, ND1000 is approximately 10 because 2 to the tenth is 1024 and nobody prints 1024.

Optical density is the base ten logarithm of the factor. ND8 is a density of 0.903 and ND64 is 1.806, so a filter printed ND 0.9 and a filter printed ND8 are the same filter. Densities add, which is convenient, and they are what you will find on cinema filter sets and gel swatch books.

And then there is the third convention, which is the one that ruins arithmetic: some makers print the stop count itself. Under that convention ND4 is four stops. Under the factor convention ND4 is two stops. Two characters, a factor of four in light, and no way to tell from the label which you are holding. If a filter's number is a power of two it is almost certainly a factor; if it is a small number like 3, 6 or 10 it is almost certainly a stop count. Almost.

Now the arithmetic the question actually wants. Nine stops is 2 to the ninth, which is 512, so an exposure of one five hundredth of a second becomes 512 over 500, which is 1.024 seconds. That is not a small aesthetic adjustment. At a five hundredth a breaking wave is a frozen sculpture with individual droplets; at a second it is a sheet of smoke. The in between values are the useful ones and they are on the chart: three stops alone takes you to a sixtieth, which is still motion with blurred edges, and six stops alone takes you to an eighth, which is where falling water starts to become a streak.

Which is why a two filter kit has three settings

Our K&F CONCEPT 4 by 5.65 inch square ND8 plus ND64 kit is a well chosen pair, and the listing is unusually helpful because it prints both notations together: a 4 by 5.65 inch ND64 at 6 stops and an ND8 at 3 stops, in its own words. Most listings print one or the other.

What makes it a kit rather than two filters is the third number, which is on neither of them. You get 3 stops, 6 stops, and 9 stops. Three operating points from two pieces of glass, spaced one and two and three units apart on a base of three, which covers the range from a slightly softened motion to a full smoothing without a gap you would notice. If the pair had been ND8 and ND16 you would have had 3, 4 and 7, which is a worse spread from the same two purchases. The pairing is the product and the arithmetic is why.

The listing also claims 0.2 percent reflectivity, which is a serious number and worth holding on to, because it comes back later. Our record notes there is no case in the box and the matte box compatibility is specific, which are real considerations for square filters. More in the K&F CONCEPT ND8 and ND64 kit review, and the field is in best camera accessories.

The variable ND, where the stops are not evenly spread

A NiSi Swift True Color ND-Vario variable ND, 67mm is the one filter on this site that publishes its range in stops rather than as a factor: one to five stops, continuously. That is the honest format, and it also lets you work out something the format hides.

A variable ND is two linear polarisers, one rotating against the other. The first one removes about half the light whatever you do, which is why the minimum setting is about one stop and never zero, and then transmission falls as the cosine squared of the angle between the two axes. Put that together and the transmission is roughly a half times cosine squared of the rotation angle.

Solve it for the ends of the published range. One stop is a half, which is zero degrees. Five stops is one thirty second, so cosine squared of the angle must be one sixteenth, the cosine must be 0.25, and the angle is 75.5 degrees. So the whole published range occupies 75.5 degrees of a possible 90.

Now ask where the next four stops would be. Nine stops needs cosine squared of one two hundred and fifty sixth, which is an angle of 86.4 degrees. So stops one to five are spread over 75.5 degrees and stops five to nine would be crammed into 10.9 degrees, a sevenfold difference in how twitchy the ring is. That is why variable NDs get unusable at the top of their travel, and it is also why the X pattern appears there: as the two polarisers approach crossed, rays arriving at different angles across a wide field see different effective angles between the axes, and the mismatch shows up as a dark cross. The listing's own feature text says the one to five stop range is deliberately capped to keep the layers away from the angle that produces an X, and the arithmetic above is what that sentence means: the cap is at 75.5 degrees, with 14.5 degrees of margin. Our record also notes the vignette free rating starts at 35mm and that five stops rules out long daylight exposures. Record in the NiSi Swift ND-Vario review, and the related category is best CPL filters for landscape photography.

You already own about seven stops, and they are not free

Our Sony E 18-135mm f/3.5 to 5.6 OSS, bundled with a filter kit publishes something most lens listings leave out: a full aperture range of f/3.5 to f/36. Work out what that is worth in stops. Light through an iris goes as the square of the diameter, so the ratio in light is the square of the ratio in f number: 36 over 3.5 is 10.29, squared is 105.8, and the base two logarithm of that is 6.73. So the iris on that lens can take away 6.7 stops all on its own, which is more than the ND64 and almost as much as the whole stack.

And it should mostly not be used that way, because of diffraction. The smallest spot a lens can form has an Airy disk whose diameter is about 2.44 times the wavelength times the f number. At 550 nanometres and f/8 that is 10.7 micrometres. At f/36 it is 48.3 micrometres. A 24 megapixel crop sensor is about 6000 pixels across a 23.5 mm width, so its pixel pitch is 3.92 micrometres: the blur circle goes from about 2.7 pixels wide to about 12.3. You have bought six stops and spent most of your resolution on them.

Which is the actual reason ND filters exist, and it is worth stating because the usual explanation is backwards. An ND filter is not there because you have run out of stops. It is there because the two other controls that remove light both do something else at the same time: the iris changes depth of field and then diffraction, and the ISO has a floor. An ND filter is the only one that changes the exposure and nothing else. Our record notes the variable aperture and the basic bundled accessories. Record in the Sony E 18-135mm with filter kit review.

The UV filter, and two numbers from one brand that cannot both be right

A K&F CONCEPT 58mm MCUV ultra slim protection filter is a different kind of object and should be judged differently. On a digital camera the sensor stack already carries a UV and infrared cut filter, so a glass UV filter in front of the lens is not performing an optical function that was missing. It is a protective window, and the right questions about a window are how flat it is, how well it is coated, and how little it costs you.

What it costs you in exposure is nothing worth measuring. The listing publishes 94 percent transmittance, and the base two logarithm of one over 0.94 is 0.089, so the filter takes away about one eleventh of a stop. You could not set that on a camera.

But hold the 94 percent next to the 0.2 percent reflectivity the same brand claims on the ND kit above, because the two cannot describe the same coating technology. A plain uncoated glass surface at a refractive index of about 1.52 reflects 4.26 percent, so bare glass with two surfaces transmits about 91.7 percent. A single magnesium fluoride layer gets you to roughly 97. A genuine broadband multilayer stack, the kind that would justify the phrase 18 layer nano coating, should be at 99 percent or better, which is what 0.2 percent per surface implies. Ninety four percent sits 2.3 points above bare glass and five points below what the coating claim promises. Our own record half notices this, listing as a drawback that some users might prefer higher transmittance while calling 94 percent decent. On the arithmetic, 94 percent is not decent for an 18 layer filter. It is roughly a single coating's worth of performance.

And that matters in exactly one situation. If each surface is reflecting around 3 percent, a ray that bounces off the back of the filter, off the front element and back out carries about 0.03 times 0.03 of the original, which is 0.09 percent, and that is 10.1 stops below the direct image. In daylight nothing in the frame is ten stops above the average, so you will never see it. At night a street lamp or a headlight is, so you get a visible ghost opposite the highlight. That is the whole story of people who insist UV filters ruin photos and people who insist they are harmless: both are right, in different light. Record in the K&F CONCEPT 58mm MCUV filter review, and the category is best camera cleaning kits.

What we left out of our own guide

Our camera accessories guide says: "for neutral density filters, consider a kit with multiple densities like ND8 and ND64, which allow you to adjust exposure for long exposures or bright conditions."

That sentence names the exact pair in the kit above and omits the only reason the pair exists. Read as written, it offers a reader two options, a weaker filter and a stronger one. In fact it offers three, because the two stack to nine stops, and the nine stop setting is the one that does the thing people buy ND filters for. The guide also never says what ND8 or ND64 mean, so a reader cannot work the third value out, and cannot tell whether a filter advertised as ND4 is two stops or four. Naming a number without its unit is the failure, and this post is the missing paragraph.

The honest limit

None of these listings publishes the two things that separate a good ND from a bad one, which are the colour cast across the visible band and the flatness of the glass. A neutral density filter is called neutral because it is supposed to attenuate every wavelength equally, and cheap ones do not: they go warm or magenta as the density rises, which is fixable in a raw file and tiresome in video. The NiSi record is the only one on this site that even names the problem, by claiming a coating designed against the yellow cast that variable NDs usually add. Nobody publishes a measured spectral transmission curve, so that claim cannot be checked from the page.

Which leaves the free moves, and for this particular problem they are unusually good.

Count the stops you already have before buying any. Dropping to your camera's base ISO is often one to two stops if you have been shooting at 400. Closing from f/5.6 to f/11 is two stops and on most lenses costs nothing visible, since the diffraction penalty above only becomes serious past about f/16. A circular polariser, if you own one, is another 1.3 to 2 stops and does something useful to reflections while it is there. That is commonly four to five stops assembled from equipment already in the bag, which is a sixtieth of a second at a five hundredth's light and already enough for softened water.

Then wait. Light falls several stops in the half hour around sunset, and waiting buys exposure and better light at the same time for nothing at all. The only thing an ND buys that patience cannot is the ability to do it at noon.

And if you have a tripod and a static frame, averaging a burst of short exposures in software reproduces much of what a long exposure does to moving water, free, with two honest caveats: it smooths motion by averaging rather than by integrating, so highlights behave differently and a bright moving object leaves a fainter trail than it would in a true long exposure, and anything that moves in the static part of the frame, like leaves, will ghost. For smooth water under a fixed horizon it is close enough that the filter is a convenience rather than a requirement, and the filter's real advantage is the one nobody mentions: it works in video, where you cannot average anything and a 9 stop stack is the only way to hold a 1/50 second shutter in daylight.