ND Filter Exposure Calculator

A neutral density filter is the plainest object in a camera bag. It is a piece of gray glass that does one thing: it throws away light. Nothing about it sharpens, saturates or corrects. Its whole purpose is to make the scene dimmer than it is.

That sounds like a strange thing to pay for until you want a slow shutter in bright light. Water only turns to silk, and clouds only streak, when the shutter stays open for seconds, and at midday no aperture or ISO setting gets you there. The filter buys the time. A well made one obstructs a controlled fraction of the light and does so evenly across the frame and, ideally, across the visible spectrum, which is where the word neutral comes from.

The arithmetic behind it is short. The trouble is the labeling. The same filter can be sold under three different numbers that look nothing alike, and two of them are easy to mistake for each other.

Stops are doublings

Photographers count light in stops. One stop is a halving or a doubling, nothing more. Exposure time relates one to one with light, so when a filter halves the light the shutter has to stay open twice as long to compensate. A one stop filter turns one second into two. A second stop doubles it again.

Because every stop is another doubling, strength grows much faster than the numbers suggest. Three stops pass one eighth of the light. Ten stops pass roughly one thousandth. One filter maker’s own table runs the sequence out to twenty stops and shows a single second becoming 1,048,576 seconds, which is about twelve days. The step from a ten stop filter to a twenty stop filter is not twice as dark. It is a thousand times darker.

The useful rule is that the new time equals the base time multiplied by two raised to the number of stops. That multiplier has its own name, the filter factor, and it is the first of the three labels.

Three names for one piece of glass

The first naming system prints the filter factor directly. ND2 halves the light, ND4 passes a quarter, ND8 passes an eighth. Read that way, ND8 is a three stop filter, because eight is two times two times two. The classic mistake is to read the number after the letters as a count of stops. An ND8 is not eight stops. It is three.

The second system uses optical density, a term borrowed from optics laboratories. Density is the base ten logarithm of the ratio of light going in to light coming out, so the fraction transmitted is ten raised to the negative density. A density of 2 passes one percent. A density of 3 passes one tenth of one percent. On a ring this appears with a decimal point: ND 0.9, ND 1.8, ND 3.0. Chemists know the same quantity as absorbance.

The third system simply states the stops, sometimes written as a three digit code that starts with 1, so that 103 means three stops and 110 means ten. Put the systems side by side and one filter reads ND8, ND 0.9, ND 103, three stops and 12.5 percent. They are all the same glass.

Here is the trap. ND8 and ND 3.0 look like neighbors. They are seven stops apart. The first is a factor of eight, a modest filter of the kind used on waterfalls. The second is a density of three, a near opaque slab for daylight. A decimal point on the ring means density. No decimal point usually means factor. A bare small number such as 3 could be either, and no rule settles it. Check the box or the maker’s chart.

The rounding nobody mentions

The three systems do not quite agree with one another, and the labels hide it. One stop is a factor of exactly two, and the base ten logarithm of two is 0.30103, not 0.3. Makers round. One of them says outright that optical density is essentially 0.3 times the stops, and the published charts of filter ratings follow that habit: 0.3, 0.6, 0.9, on up to 3.0 for ten stops.

Take the label literally and a density of 3.0 passes exactly one thousandth of the light, which is 9.966 stops, not ten. Ten true stops would be a factor of 1,024 and a density of 3.01. This is also why the ten stop filter is called ND1000 in one place and ND1024 in another. The published tables list them as the same filter, one name rounded for the eye and one computed from the doublings.

Does it matter? Hardly. The gap between 1,000 and 1,024 is about a thirtieth of a stop, and high precision is rarely needed with these filters: a whole stop either way often changes the picture very little. What matters is knowing that the rounding exists, so that two calculators giving 16.67 and 17.07 seconds for the same shot do not look like a disagreement about physics. They are a disagreement about which label to believe.

Stacking, and a worked example

Filters in series multiply. Their factors multiply, which means their stops add and their densities add. This is the real convenience of the logarithmic label: to find the strength of a stack, add the numbers printed on the rings.

Suppose the meter gives 1/60 second at the aperture and ISO you want, and you fit a ten stop filter. Two to the tenth is 1,024, and 1,024 divided by 60 is 17.07 s. Now stack a three stop and a six stop filter in front of it. The total is 19 stops, the factor is 524,288 and the density is 5.72. The same 1/60 second becomes 8,738 seconds, which is 2 hours 25 minutes 38 seconds. Nineteen stops is a great deal of darkness.

When the stack overshoots, the other two exposure controls can pull it back, because they count in stops too. Each stop of aperture changes the light by a factor of two, and so does each doubling of the ISO number. Opening the lens by one stop halves the time. So does doubling the ISO.

Stacking has costs that the arithmetic does not show. No filter is perfectly neutral, and cheaper ones in particular can leave a color cast. A cast that follows the white balance is easy to remove afterward, while a severe one can be much harder to correct. The cause is simple: a real filter does not dim every wavelength by the same amount. Stacking can also reduce image quality, which is one reason strong single filters exist at all.

Film does not count the way a sensor does

A sensor takes the multiplied time more or less at face value. Film does not. At long exposures and low light levels, film responds less than the arithmetic predicts, an effect its makers call reciprocity failure. The remedy is more time, and how much depends on the emulsion.

A simple model, set out in Wikipedia’s article on reciprocity, uses a single exponent. The corrected time is the metered time in seconds raised to a power, and the rule is meant for times longer than one second. Typical exponents run from 1.25 to 1.45, with some as low as 1.1 and some as high as 1.8. For a film with a factor of 1.31, a metered 10 seconds becomes 20.4 s. The same article adds a caution: no constant exponent has replaced measured data for the material in hand.

The lesson is that there is no universal reciprocity number. Use the figure on the data sheet for the film in the camera. Guessing from a different film is how a carefully computed two minute exposure comes back thin.

Digital cameras have their own long exposure penalty. One camera manual describes a setting that reduces the noise, bright dots or banding, that tends to appear at shutter speeds of one second or slower. The processing happens after the shot and can take as long as the exposure itself, which doubles the wait for each picture.

Before the glass goes on

A ten stop filter is close to opaque. With it in place you often cannot see anything through the lens, so the order of work matters. Compose first. Focus, then switch to manual focus so the camera cannot hunt. Take the meter reading without the filter. Only then fit the glass and multiply. Cover the eyepiece on a camera with an optical viewfinder. Stray light entering from behind can affect a meter reading taken through the filter.

For exposures longer than 30 seconds the usual tool is bulb mode, where the shutter stays open for as long as the release is held. Some cameras offer a bulb timer that holds the exposure for a set duration, and a lockable remote release saves a tired thumb on the rest. Either way you need a clock you can read in the dark.

No calculation can tell you what the filter really is. Labels are rounded, as shown above, and even a laboratory supplier quotes its densities at one wavelength and publishes tolerances for them. The honest method is a test pair: one frame without the filter, one with it, adjusted until the two match. The ratio of the two times is the factor of your filter. Write it on the case.