How To Calculate Long Exposure Times + Free Download

Note: If you’re not after the theory, and just want the free downloadable PDF of the long exposure charts then you’ll find the link towards the bottom of the page.

In order to calculate the exposure time when using a specific type of neutral density filter, it’s also a good idea to have an understanding about how we label these ND filters. You might first want to take a look through my previous post: Understanding Neutral Density Filter Names and Numbers if you are unsure about that topic.

Long Exposure Photography Formulas

t_ND = t₀ x 2^ND

Where:

• ND = F-Stop reduction in light from filter
• t_ND = Final exposure time in seconds
• t₀ = Correct exposure time without ND filter

In this simplified formula, we need to know the reduction in light that our filter gives us in f-stops. Sometimes that f-stop reduction isn’t mentioned on the filter, or even the packaging for the filter, and this is where we need to know how to convert a filter’s optical density number, into an f-stop. This mathematical process was covered extensively in my previous post about the naming of neutral density filters, but for simplicity, I’m also just going to include the conversion table below.

To understand this long exposure formula a little bit more, we need to remember the key definition that one f-stop is either a doubling, or a halving of a particular amount of light. An increase of one stop indicates a doubling of the light, and a decrease of one stop indicates a halving of the amount of light. If we use a 1-stop ND filter on a lens, it is reducing the light coming into the lens by one stop, in other words it is halving the light coming through it. A 2-stop ND filter reduces the light by 4 times (2×2) and a 3-stop filter reduces the light by 8 times (2x2x2), and so on. This can be expressed mathematically by what we call the “Filter Factor” which is what you see on the right-hand side of our long exposure formula: 2^ND

Sometimes this Filter Factor number is actually displayed on the filter ring, or the filter case, usually expressed with the letters ND followed by a number. eg. ND8 or ND32. In this case you can just use the simplified long exposure formula:

t_ND = t₀ x Filter Factor

Example

A 5-stop reduction in light would give us a filter factor of 2⁵ = 2x2x2x2x2 = 32 , so an ND32 is also called a 5-stop neutral density filter. If your exposure was 1 second before applying the 5-stop ND filter, we can now see that your new exposure time is going to be 32 times longer, i.e. 32 seconds.

What About Calculating Exposure Time With Optical Density?

We can create a new variation on this equation for use with optical density (d) instead of f-stop. The optical density of a filter is probably the most common way for a filter to be labelled, so if you’ve ever seen a filter labelled as a 0.9 ND filter, the 0.9 is the optical density number of that filter. The table below will show you all the optical densities converted into f-stops if you’d prefer to think of them that way.

We know from my previous post about calculating optical density numbers, that d = log₁₀Filter Factor

Using the inverse log process, this tells us that Filter Factor = 10^d

Now we get the third way to express the new long exposure time by substituting that into our original equation to get:

t_ND = t₀ x 10^d

Where:

• d = Optical Density number of a filter (e.g 0.3, 0.9, 1.2 etc.)
• t_ND = Final exposure time in seconds
• t₀ = Correct exposure time without ND filter

Example

Sticking with the numbers from the previous example, let’s look at a 1 second exposure with a 5-stop ND filter applied to it. Using the table below, we can see that a 5-stop filer has an optical density of 1.5. Plugging this into the new variation of our formula gives us t_ND = 1 x 10^1.5 = 31.6 seconds which we round to 32 seconds. The same answer as last time, as we expected. The variation in 31.6 vs exactly 32 seconds comes from the fact that actually, the optical density of a 5-stop filter is 1.50514997832 (from log₁₀ 2⁵ ), but we round it down to 1.5 for simplicity when describing filters. If you ran the equation as t_ND = 1 x 10^{1.50514997832} then you would get exactly 32 seconds without needing to round it up at the end.

Converting Optical Density Number Into F-Stop Reduction

As you can see from this table, it might get a bit confusing if you aren’t careful. A filter might have the number 4 on the side of it, and you could mistakenly think this this means it will provide a 4-stop reduction in light. In fact, it’s more likely this number is referring to optical density, which would mean that it would deliver a 13-stop reduction in light, and there’s always the curve ball that the manufacturer is quoting filter factor without using the “ND” prefix, in which case a 4 would mean a 2-stop reduction in light!

In reality, filter manufacturers these days usually use optical density, and if they are directly quoting differences in f-stops, then they will use the term “f-stop” quite clearly. The other reality is that a 2-stop ND filter and a 13-stop ND filter look very different to the eye. A 2-stop filter is still letting half the light through, so it’s relatively translucent. On the other hand, a 13-stop filter is only letting 0.012% of the light through, so it’s going to appear completely black and opaque.

If you don’t want to calculate the various varieties of names for filters, this table will give you all of the most commonly used ones:

Of course filter manufacturers could create neutral density filters with any amount of opacity they please, but they create them in these 1-stop increments so that we can easily calculate relative exposures.

Long Exposure Charts

IMPORTANT NOTE: To make these fit nicely on a web page, I’ve split them up a bit, so make sure you scroll down to find the ND filter you’re looking for. For all exposure values under and including 30 seconds, i.e. those which are selectable in camera without the use of bulb mode, I have rounded the results to use the standard set of available shutter speeds in modern cameras. Once we have gone over 30 seconds, I have left the results in hours, minutes and seconds. For larger values, this is in reality more accurate than is necessary because this would assume a perfect filter from the manufacturer. As filter factor increases, it becomes harder and harder for manufacturers to be precise about the filter’s optical density. When you couple this with changing ambient light over the period of your exposure, you really have to take longer exposure values as a starting point, and often make adjustments on the fly depending on weather and the specifics of your filter. Rounding the result to the nearest minute would be just fine. Also note that very obviously, some of these exposure times are ludicrous, but instead of leaving them out and having blank cells I thought I might as well keep them there. I highly doubt that any of you are going to make a 22 day long exposure, but I’d love someone to prove me wrong!

IMPORTANT NOTE #2: The reason that I decided to make these charts in the first place was that I could not find a satisfactory set available from anywhere else online. Yes, there are a few, but all of them are heavily simplified and either didn’t have the neutral density range I was looking for (up to 16-stops), or omitted many of the regularly selectable shutter speeds in order to make the tables more compact and easier on the eye. At least I presume that is their reasoning. I believe my set of long exposure tables to be much more complete, and I’m glad to offer them as a free download in PDF format as well.

1-stop ND to 5-stop ND

6-stop ND to 10-stop ND

11-stop ND to 16-stop ND

Are You Stacking Filters Together?

A frequently asked question in the realm of long exposure photography is “what happens when I stack fitlers together?”

Thankfully the answer is very simple; You simply add the f-stop values of each filter together to get the final resulting reduction in f-stops. If you stack a 6-stop filter and a 4-2top filter then you’ll have the equivalent of a 10-stop filter. Be warned though, the more filters you stack together, the more vignetting you’ll get in the corners of your image. Always use the minimum number of ND filters to achieve your goal. If you have a 2-stop, 3-stop, 4-stop, 5-stop and a 6-stop filter, don’t stack the 2,3 and 5 to get to 10! Just use the 4 and the 6.

Let’s Do an Example

You are setting up a beautiful landscape shot and you’d like to capture the swirling movement of the clouds by using a much longer exposure than is natively possible with your lens. You set your camera up on a tripod, and expose the scene correctly without an ND filter in place.

Your chosen exposure is f/11, ISO100, 0.3 seconds

You have a filter in your bag that says 3.0 on the side of the filter ring. Consulting the first conversion table on the page, we can see that this is a 10-stop ND filter, which should work very well for this purpose.

If you want to use the formula, it would be t_ND = 0.3 x 2¹⁰ = 307.2 seconds = 5 minutes and 7 seconds.

If you want to use the log exposure chart, simply find the row in the first column that’s labelled 0.3, and then follow it over to the column that’s labelled 10-stops.

FREE Download – Long Exposure Chart PDF

Lots of people rely on mobile apps these days to help them calculate their long exposure values, but this can be problematic in cold weather which can often cause mobile device batteries to shut down prematurely. For this reason, I always recommend that you have a printed long exposure chart tucked away somewhere in your camera bag. This free downloadable long exposure chart PDF is split up into several sections so that you can print the ones that are relevant to you and your selection of ND filters. You can either choose to have the full table with all ND values, or choose pages that only show specific, common ND filter sets used by many landscape photographers.