Long Exposure Math: ND Filters and Shutter Time

How does a shot metered at 1/125 second become an 8-second exposure? A 10-stop neutral density filter does it, and the math takes one line. Each stop of filter doubles the shutter time, so 10 stops multiply it by 1,024. Once you see that pattern, every filter box label and every long exposure starts to make sense.

What Does an ND Filter Actually Do?

An ND filter is dark, neutral glass that cuts the light reaching the sensor without changing its color. Less light means you need a longer shutter time for the same exposure. That longer time is what turns moving water silky and makes clouds streak.

Filter strength is counted in stops. One stop is half the light, so each stop of filter asks you to double the shutter time. Stops are the same unit used for aperture and ISO, as explained in our guide to the exposure triangle.

The doubling adds up fast. Three stops make the exposure 8 times longer. Six stops make it 64 times longer, and ten stops make it 1,024 times longer. A strong filter turns a crisp daylight frame into several seconds of motion.

How Do ND Numbers, Stops and Density Connect?

They are three labels for the same light cut, written on different scales. The ND number is the multiplier, stops are its power of 2, and optical density is its power of 10.

The Three Formulas

Stops equal log2 of the ND number, so an ND64 is 6 stops. Optical density equals log10 of the ND number, so an ND1000 is density 3.0. Optical density and transmission follow T = 10 to the power of minus OD, per the Edmund Optics note.

Each 0.3 of density is almost exactly one stop, since the true figure is 0.301. So ND 0.9 means 3 stops and ND 1.8 means 6 stops. The new shutter time is then the base time times 2 to the power of the stops.

An ND1000 is really 9.97 stops. Treating it as a round 10 stops changes the time by only 2.4 percent, which no camera can see.

A Worked Example at the Waterfall

Picture a bright waterfall in midday sun. With no filter, the meter reads f/8 at 1/125 second at ISO 100. You want the water fully smooth, so you pick a 10-stop filter.

Work it in three steps. First, 2 to the power of 10 is 1,024. Second, 1/125 of a second is 0.008 second. Third, 0.008 times 1,024 is 8.19 seconds, so you set 8 seconds on the dial.

Now try a gentler look. A 6-stop ND64 multiplies the time by 64, giving 0.512 second. That softens the water but keeps some texture in the spray.

Last, a cloudy scene meters at 1/60 second. The same 10-stop filter gives 1/60 times 1,024, or 17.07 seconds. Your camera offers 15 or 20 seconds, and both sit within a quarter stop of the math. Pick 20 seconds when the histogram looks dark.

What Happens Past 30 Seconds?

Most cameras stop their timed shutter speeds at 30 seconds. Anything longer needs Bulb mode, where the shutter stays open while you hold the release. A remote or an intervalometer then times the exposure for you.

You hit that wall sooner than you expect. With 10 stops, any base slower than about 1/34 second passes 30 seconds. A base of 1/15 second becomes 68.3 seconds, and a base of 1/8 second becomes 128 seconds, or 2 minutes 8 seconds.

Stacking Filters

Stacked filters add their stops, and their densities add too. An ND8 plus an ND64 gives 3 + 6 = 9 stops, a multiplier of 512, and density 2.7. From 1/60 second, that stack gives 8.53 seconds.

Film and Reciprocity Failure

On film, the doubling rule breaks down at long times, an effect called reciprocity failure. The film needs extra time beyond the math. Digital sensors avoid this but gain noise from dark current during very long exposures.

Mistakes That Ruin Long Exposures

Most failed long exposures come from setup habits, not from the math. These five slip-ups cause most of the trouble.

• Metering through a strong filter. A 10-stop filter leaves only 0.1% of the light, which confuses many meters. Meter first, then fit the filter.
• Focusing after the filter goes on. The view goes nearly black, so autofocus hunts. Focus first, switch to manual focus, then mount the filter.
• Forgetting the viewfinder. Stray light can leak in through an optical eyepiece during long exposures. Cover it with its cap or your hand.
• Counting ND numbers as stops. An ND8 is 3 stops, not 8. Adding ND8 and ND64 as “72” gives nonsense; add 3 and 6 stops instead.
• Skipping the tripod and remote. Any touch during an 8-second exposure blurs the whole frame. Use a solid tripod and a remote or a 2-second timer.

Which Filter Strength Fits Your Shot?

Choose the strength by working backward from the time you want. Stops needed equal log2 of target time divided by base time. Round to the nearest filter you own or can stack.

Say you want 2 seconds of flowing water and the base is 1/125 second. That is 250 times longer, which is 7.97 stops, so 8 stops fits. An ND256, or an ND64 stacked with an ND4, does the job.

Streaking clouds need more time. From a 1/60 second base, a full minute is 11.8 stops. A 10-stop filter gives 17 seconds, and closing the aperture from f/8 to f/16 adds 2 more stops for 68.3 seconds in Bulb mode.

As a rough guide, 3 to 6 stops suit softened water and motion blur. Ten stops suits smooth seas and cloud trails. Very dense filters around 16 stops smooth long daytime scenes. Check any combination with the long exposure time calculator before you head out.

Never aim a camera at the sun with a standard ND filter. NASA eclipse guidance notes that proper solar filters cut the sun’s visible and infrared energy by a factor of 100,000.

Common Questions About Long Exposures and ND Filters

References

This guide covers the exposure math for ND filters and long shutter times. Real filters vary slightly from their rating, so confirm the first frame on your histogram. Reviewed for accuracy by Prof. Dr. Khalil Mudassar, PhD. Last updated September 27, 2026.