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

tND = t0 x 2ND

Where:

  • ND = F-Stop reduction in light from filter
  • tND = 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: 2ND

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:

tND = t0 x Filter Factor

Example

A 5-stop reduction in light would give us a filter factor of 2= 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 = 10d

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

tND = t0 x 10d

Where:

  • d = Optical Density number of a filter (e.g 0.3, 0.9, 1.2 etc.)
  • tND = 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 tND = 1 x 101.5 = 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 2), but we round it down to 1.5 for simplicity when describing filters.  If you ran the equation as tND = 1 x 101.50514997832 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:

F-Stop ReductionOptical DensityFilter Factor% transmittance
000100
10.3250
20.6425
30.9812.5
41.2166.25
51.5323.125
61.8641.5625
72.11280.78125
82.42560.390625
92.75120.1953125
103.01024 (sometimes called ND1000)0.09765625
113.320480.048828125
123.640960.0244140625
133.981920.01220703125
13 1/34.0100000.01
144.2163840.006103515625
154.5327680.003051757813
164.8655360.001525878906
16 2/35.01000000.001
175.11310720.0007629394531
185.42621440.0003814697266
195.75242880.0001907348633
20610485760.00009536743164

 

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

Indicated Shutter Speed

1-stop

2-stop

3-stop

4-stop

5-stop

1/80001/40001/20001/10001/5001/250
1/64001/32001/16001/8001/4001/200
1/50001/25001/12501/6401/3201/160
1/40001/20001/10001/5001/2501/125
1/32001/16001/8001/4001/2001/100
1/25001/12501/6401/3201/1601/80
1/20001/10001/5001/2501/1251/60
1/16001/8001/4001/2001/1001/50
1/12501/6401/3201/1601/801/40
1/10001/5001/2501/1251/601/30
1/8001/4001/2001/1001/501/25
1/6401/3201/1601/801/401/20
1/5001/2501/1251/601/301/15
1/4001/2001/1001/501/251/13
1/3201/1601/801/401/201/10
1/2501/1251/601/301/151/8
1/2001/1001/501/251/131/6
1/1601/801/401/201/101/5
1/1251/601/301/151/81/4
1/1001/501/251/131/60.3
1/801/401/201/101/50.4
1/601/301/151/81/40.5
1/501/251/131/60.30.6
1/401/201/101/50.40.8
1/301/151/81/40.51
1/251/131/60.30.61.3
1/201/101/50.40.81.6
1/151/81/40.512
1/131/60.30.61.32.5
1/101/50.40.81.63.2
1/81/40.5124
1/60.30.61.32.55
1/50.40.81.63.26
1/40.51248
0.30.61.32.5510
0.40.81.63.2613
0.5124815
0.61.32.551020
0.81.63.261325
12481530
1.32.55102042
1.63.26132551
24815301m 4s
2.551020401m 20s
3.261325511m 42s
4815301m 4s2m 8s
51020401m 20s2m 40s
61325481m 36s3m 12s
815301m 4s2m 8s4m 16s
1020401m 20s2m 40s5m 20s
1325521m 44s3m 28s6m 56s
15301m2m4m8m
20401m 20s2m 40s5m 20s10m 40s
25501m 40s3m 20s6m 40s13m 20s
301m2m4m8m16m

Indicated Shutter Speed

1-stop

2-stop

3-stop

4-stop

5-stop

 

6-stop ND to 10-stop ND

Indicated Shutter Speed

6-stop

7-stop

8-stop

9-stop

10-stop

1/80001/1251/601/301/151/8
1/64001/1001/501/251/131/6
1/50001/801/401/201/101/5
1/40001/601/301/151/81/4
1/32001/501/251/131/60.3
1/25001/401/201/101/50.4
1/20001/301/151/81/40.5
1/16001/251/131/60.30.6
1/12501/201/101/50.40.8
1/10001/151/81/40.51
1/8001/131/60.30.61.3
1/6401/101/50.40.81.6
1/5001/81/40.512
1/4001/60.30.61.32.5
1/3201/50.40.81.63.2
1/2501/40.5124
1/2000.30.61.32.55
1/1600.40.81.63.26
1/1250.51248
1/1000.61.32.5510
1/800.81.63.2613
1/60124815
1/501.32.551020
1/401.63.261325
1/302481530
1/252.55102041
1/203.26132551
1/154815301m 8s
1/1351020391m 19s
1/1061325511m 42s
1/8815301m 4s2m 8s
1/61020431m 25s2m 51s
1/51325511m 42s3m 25s
1/415301m 4s2m 8s4m 16s
0.320381m 17s1m 34s5m 7s
0.425511m 42s3m 25s6m 50s
0.5301m 4s2m 8s4m 16s8m 32s
0.6381m 17s1m 34s5m 7s10m 14s
0.8511m 42s3m 25s6m 50s13m 39s
1s1m 4s2m 8s4m 16s8m 32s17m 4s
1.3s1m 23s2m 46s5m 32s11m 6s22m 11s
1.6s1m 42s3m 25s6m 50s13m 39s27m 18s
2s2m 8s4m 16s8m 32s17m 4s34m 8s
2.5s2m 40s5m 20s10m 40s21m 20s42m 40s
3.2s3m 25s6m 50s13m 39s27m 18s54m 37s
4s4m 16s8m 32s17m 4s34m 8s1h 8m 16s
5s5m 20s10m 40s21m 20s42m 40s1h 25m 20s
6s6m 22s12m 48s25m 36s51m 12s1h 42m 24s
8s8m 32s17m 4s34m 8s1h 8m 16s2h 16m 32s
10s10m 40s21m 20s42m 40s1h 25m 20s2h 50m 40s
13s13m 52s27m 44s55m 28s1h 50m 56s3h 41m 52s
15s16m32m1h 4m2h 8m4h 16m
20s21m 20s42m 40s1h 25m 20s2h 50m 40s5h 41m 20s
25s26m 40s53m 20s1h 46m 40s3h 33m 20s7h 6m 20s
30s32m1h 4m2h 8m4h 16m8h 32m

Indicated Shutter Speed

6-stop

7-stop

8-stop

9-stop

10-stop

 

11-stop ND to 16-stop ND

Indicated Shutter Speed

11-stop

12-stop

13-stop

14-stop

15-stop

16-stop

1/80001/40.51248
1/64000.30.61.32.5510
1/50000.40.81.63.2613
1/40000.5124815
1/32000.61.32.551020
1/25000.81.63.261325
1/200012481530
1/16001.32.55102041
1/12501.63.26132552
1/100024815301m 6s
1/8002.551020411m 22s
1/6403.261325511m 42s
1/5004815301m 6s2m 11s
1/40051020411m 22s2m 44s
1/32061325511m 42s3m 25s
1/250815301m 6s2m 11s4m 22s
1/2001020411m 22s2m 44s5m 28s
1/1601325511m 42s3m 25s6m 50s
1/12515301m 6s2m 11s4m 22s8m 44s
1/10020411m 22s2m 44s5m 28s10m 55s
1/8025511m 42s3m 25s6m 50s13m 39s
1/60301m 8s2m 17s4m 33s9m 6s18m 12s
1/50411m 22s2m 44s5m 28s10m 55s21m 51s
1/40511m 42s3m 25s6m 50s13m 39s27m 18s
1/301m 8s2m 17s4m 33s9m 6s18m 12s36m 25s
1/251m 22s2m 44s5m 28s10m 55s21m 51s43m 41s
1/201m 42s3m 25s6m 50s13m 39s27m 18s54m 37s
1/152m 17s4m 33s9m 6s18m 12s36m 25s1h 12m 49s
1/132m 38s5m 15s10m 30s21m42m 1s1h 24m 1s
1/103m 25s6m 50s13m 39s27m 18s54m 37s1h 49m 14s
1/84m 16s8m 32s17m 4s34m 8s1h 8m 16s2h 16m 32s
1/65m 41s11m 23s22m 45s45m 31s1h 31m 1s3h 2m 3s
1/56m 50s13m 39s27m 18s54m 37s1h 49m 14s3h 38m 27s
1/48m 32s17m 4s34m 8s1h 8m 16s2h 16m 32s4h 33m 4s
0.310m 14s20m 29s40m 58s1h 21m 55s2h 43m 50s5h 27m 41s
0.413m 39s27m 18s54m 37s1h 49m 14s3h 38m 27s7h 16m 54s
0.517m 4s34m 8s1h 8m 16s2h 16m 32s4h 33m 4s9h 6m 8s
0.620m 29s40m 58s1h 21m 55s2h 43m 50s5h 27m 41s10h 55m 22s
0.827m 18s54m 37s1h 49m 14s3h 38m 27s7h 16m 54s14h 33m 49s
1s34m 8s1h 8m 16s2h 16m 32s4h 33m 4s9h 6m 8s18h 12m 16s
1.3s44m 22s1h 28m 45s2h 57m 30s5h 54m 59s11h 49m 58s23h 39m 57s
1.6s54m 37s1h 49m 14s3h 38m 27s7h 16m 54s14h 33m 49s29h 7m 38s
2s1h 8m 16s2h 16m 32s4h 33m 4s9h 6m 8s18h 12m 16s36h 24m 32s
2.5s1h 25m 20s2h 50m 40s5h 41m 20s11h 22m 40s22h 45m 20s45h 30m 40s
3.2s1h 49m 14s3h 38m 27s7h 16m 54s14h 33m 49s29h 7m 38s58h 15m 16s
4s2h 16m 32s4h 33m 4s9h 6m 8s18h 12m 16s36h 24m 32s72h 49m 4s
5s2h 50m 40s5h 41m 20s11h 22m 40s22h 45m 20s45h 30m 40s91h 1m 20s
6s3h 24m 48s6h 49m 36s13h 39m 12s27h 18m 24s54h 36m 48s109h 13m 36s
8s4h 33m 4s9h 6m 8s18h 12m 16s36h 24m 32s72h 49m 4s145h 38m 8s
10s5h 41m 20s11h 22m 40s22h 45m 20s45h 30m 40s91h 1m 20s182h 2m 40s
13s7h 23m 44s14h 47m 28s29h 34m 56s59h 9m 52s118h 19m 44s236h 39m 28s
15s8h 32m17h 4m34h 8m68h 16m136h 32m273h 4m
20s11h 22m 40s22h 45m 20s45h 30m 40s91h 1m 20s182h 2m 40s364h 5m 20s
25s14h 13m 20s28h 26m 40s56h 53m 20s113h 46m 40s227h 33m 20s455h 6m 40s
30s17h 4m34h 8m68h 16m136h 32m273h 4m546h 8m

Indicated Shutter Speed

11-stop

12-stop

13-stop

14-stop

15-stop

16-stop

 

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 tND = 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

long exposure charts

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.

REP005

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