ND Filter Long Exposure Calculator
Turn a shutter speed and an ND filter into the exposure time you actually need — entered as filter number, density or stops, and snapped to the nearest setting on a real shutter dial.
About this tool
An ND filter is sold under three different labels that all describe the same piece of glass. The number on the rim, like ND8, says how many times it cuts the light. The density figure, like 0.9, is an optical density on a logarithmic scale. And photographers often just talk in stops. Because the relationship between them is logarithmic, the numbers look nothing like each other: the same filter is ND8, density 0.9 and 3 stops.
That is where most calculators and most quick mental arithmetic go wrong. ND8 is not eight stops, it is three — 2 to the power of 3 is 8. ND1000, universally sold as a ten-stop filter, is really 9.97 stops; the value that lands exactly on ten is ND1024. A filter marked ND400 is 8.64 stops, not nine. Enter the number here and the tool does the logarithm, then shows all three labels side by side so you can see what your own filter really is.
The second thing that gets lost is that a camera shutter dial is not a continuous scale. Suppose the metered exposure is 1/125 s and you screw on an ND1000: the maths gives 8 seconds, which the dial does have. But the same filter on a 1/60 s reading gives 16.67 seconds, and no camera has that setting. The nearest marked value is 15 seconds, a sixth of a stop under. The tool rounds to the nearest real setting and tells you how far off that is, so you are choosing a dial position rather than a number you cannot enter. The marked values themselves are not evenly spaced either — the marking says 1/8 s where the physical speed is 1/7.5 s, and 15 s means about 16 s. That is the camera maker rounding the label, not an error here.
Finally, shutter dials stop at 30 seconds. Any longer exposure is done in Bulb mode, where the shutter stays open as long as you hold it, and you time it with a phone or a remote release. A calculator that quietly caps the answer at 30 seconds is telling you to underexpose by several stops without saying so, so this one says plainly that the exposure is beyond the dial and gives you the time to count.
Why the nearest dial setting is measured in stops
The closest marked shutter speed is chosen by comparing the ratio of the two times, not the difference in seconds. Time on a camera is exponential, so one stop away is a doubling away at every point on the dial, fast end and slow end alike.
A dial is a list of doublings, so the meaningful distance between two settings is how often one would have to be doubled to reach the other. Measured in seconds instead, the gaps at the fast end become almost invisible while the gaps at the slow end look enormous.
Take a computed 0.0002 s. It is 0.00005 s away from 1/4000 and 0.0003 s away from 1/2000, so subtraction would pick 1/4000. Measured in stops it sits far closer to the 1/5000 region, and a dial that carried that position would be the better setting to use.
The answer comes with the offset in stops, sign included. A negative offset means the setting is faster than the exact time needs, which pushes the frame toward underexposure; a positive one is the opposite. That is the number worth carrying in your head, rather than a count of seconds.
Exactly 30 seconds is not Bulb
A shutter dial runs to 30 seconds, and only an exposure longer than that is flagged as needing Bulb. A combination that lands exactly on 30 s is left alone, even though the arithmetic in floating point can settle on either side of it.
The boundary is where two decimal representations disagree. One eighth of a second multiplied by 240 is exactly 30 on paper, but the stored values produce 30.000000000000004 — and a strict comparison would announce that the filter has pushed the exposure past the end of the dial.
The mirror image happens too: 1/125 s with a factor of 3750 comes out at 29.999999999999986, edging the other way. A tolerance of one millionth of a second sits at the boundary so that both of these land on the correct side of it.
That tolerance is not slack for unsteady hands. It is a million times smaller than any precision a photograph could care about, and it exists only to stop rounding noise from being read as a real difference in exposure.
Why the starting shutter speed must be a real dial setting
The exposure you start from has to be one of the settings the camera actually has. A metered 1/63 s is rejected, because no shutter dial carries that value and the whole point of the result is to name a position you can turn to.
A meter reports whatever the light gives it, and that is not a list a camera can be set to. The tool maps the value onto the nearest marked speed and accepts it only when it matches one closely, so the starting point is always a real position on the dial.
This is what makes the answer usable. The exact time, the nearest setting and the offset in stops are all stated relative to a speed you can reproduce on the camera, rather than to a number the meter invented.
The dial runs from 1/8000 s to 30 s. Beyond that the shutter dial is no longer the instrument in play, which is exactly the line that Bulb mode crosses.
ND1000 is 9.97 stops, and the round ten stops is ND1024
Three markings on a filter describe one piece of glass. Stops are the logarithm of the factor, so a ten-stop filter is 2 to the tenth, which is 1024 times, not 1000.
Run the table here: ND2 is 1 stop, ND8 is 3, ND64 is 6, ND1000 is 9.966, ND1024 is exactly 10, and ND10000 is 13.288. Only the powers of two land on whole stops, which is why the round numbers on packaging and the round numbers on a light meter are two different sets.
Density is the same quantity written in base ten. Density 0.9 converts to 2.99 stops and back to 8 times, density 3.0 to 9.966 stops and 1000 times, density 4.0 to 13.288 stops and 10000 times. Every third of a density unit is one stop, because 2 to the tenth is a thousand and a thousand is three decimal digits.
So a filter marked ND1000, one marked ND 3.0 and one marked 9.97 stops are the same object, while a filter advertised as ten stops is a different, slightly darker one. That distinction only shows up when the result is compared against a metered time: one third of a stop is a 26 percent difference in exposure, which is visible.
Frequently asked questions
What does the number on an ND filter mean?
It is the factor by which the filter dims the light. ND8 passes one eighth of the light, so it costs you three stops. The number is not the stop count: the stops are the base-2 logarithm of it. That is why ND2, ND4 and ND8 are one, two and three stops.
How many stops is an ND1000?
9.97, usually rounded to ten. The exact ten-stop factor is 1024, and a few makers do sell that. Using ten instead of 9.97 changes the exposure by a hundredth of a stop, which is invisible in practice, but it is worth knowing that the round number on the box is not the exact one.
What is the density rating for?
It comes from the optical industry rather than photography: density is the base-10 logarithm of the factor, so a ten-stop filter is density 3.0 and a six-stop filter is 1.8. It is the same information as the number on the rim, written on a different scale. Entering either here gives the same result.
Why is the result rounded?
Because it has to be. A metered 1/60 s with a ten-stop filter needs 16.67 seconds, and no shutter dial has that position. The tool shows the exact time and, separately, the nearest setting your camera really has, with the difference in stops. One third of a stop is the usual tolerance for slide film and is nothing on digital.
How do I shoot exposures longer than 30 seconds?
In Bulb mode. The shutter stays open while the release is held, so you time the exposure yourself with a phone stopwatch or an intervalometer. The calculator tells you when the answer has crossed that line and how long to count.
Do I need a tripod?
For anything with an ND filter, in practice yes. The tool flags it when the resulting exposure is slower than the usual hand-holding limit of about 1/60 s, which any filter stronger than a stop or two will reach immediately.
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