ND filter exposure calculator for long exposures

What this calculator does

Neutral density filters are labelled three different ways and the numbers look nothing alike. A ten-stop filter, an ND1000 and a 3.0 density are all very nearly the same piece of glass, and a photographer who owns one of each has no obvious way to tell. This takes whichever label is on your filter and works out the shutter speed.

The arithmetic is doubling. Each stop doubles the exposure time, so ten stops multiply it by 1,024. A metered 1/125 of a second becomes 8.2 seconds, which is the difference between a snapshot and water turning to mist.

The formula

Formulanew shutter = base shutter × 2^stops. An ND number is 2^stops, and an optical density is stops × log₁₀2, which is why ND1000 and 3.0 both mean about ten stops

Stops are the natural unit, because each one doubles the time: new shutter = base × 2^stops. An ND number is the light reduction factor, which is 2^stops, so ND1000 is about ten stops rather than exactly ten. An optical density is the base-ten logarithm of that factor, so a density of 3.0 means a thousandfold reduction, which again is 9.97 stops. All three describe the same glass.

Term	Meaning
Stop	A doubling or halving of light. The unit everything here converts into.
ND number	The factor by which light is cut. ND8 passes an eighth, which is three stops.
Optical density	Log base ten of that factor. A density of 0.9 is ND8 is three stops.
Stacking	Filters used together add their stops, so a six-stop and a three-stop give nine.

The inputs explained

Field	What to enter
Shutter speed without the filter (s)	The shutter speed your camera meters without the filter, in seconds. A 1/125 is 0.008.
How the filter is labelled	Pick whichever way your filter is marked. The three are different labels for the same property.
The number on the filter	The number printed on the filter: 10 for a ten-stop, 1000 for an ND1000, 3.0 for a density.
A second filter stacked (stops)	Stops from a second filter if you are stacking. Always in stops, whatever the first filter is labelled in.

When to use it

Working out a long exposure in the field

Meter the scene without the filter, read off the shutter speed, then fit the filter and use the result. Metering through a ten-stop filter rarely works because the camera cannot see enough light to measure.

Checking whether two filters are the same

Enter an ND1000 and then a 3.0 density. Both come out at 9.97 stops, which is how you tell that two filters labelled completely differently are interchangeable.

Stacking to reach a longer exposure

The stops add rather than multiply. A six-stop plus a three-stop is nine stops, not eighteen, and the result is 512 times the base exposure rather than 262,144.

Worked examples

Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.

What does each filter strength do to 1/125 of a second?

Only the filter strength changes.

Metered at 1/125s without the filter

Filter	Shutter speed with the filter	Equivalent ND number	Light that gets through
1 stops	1/63 s	ND2	50.0%
3 stops	1/16 s	ND8	12.5%
6 stops	1/2 s	ND64	1.56%
10 stops	8.19 s	ND1,024	0.098%
13 stops	1:06 (66 s)	ND8,192	0.012%
15 stops	4:22 (262 s)	ND32,768	0.003%

Three stops takes 1/125 to 1/16 of a second, which is enough to blur a waterfall and not much else. Six stops reaches half a second. Ten stops is 8.19 seconds and the common choice for smoothing water and cloud. Fifteen stops is 4 minutes 22 seconds, which is daylight long exposure territory where people disappear from the frame entirely.

Do the three labelling systems agree?

Each row is a filter as it might actually be marked.

The same base exposure, filters described three ways

Number on the filter	Stops of light removed	Equivalent ND number	Equivalent optical density
3	3.00	ND8	0.90
6	6.00	ND64	1.81
10	10.00	ND1,024	3.01

Read as stops, the numbers 3, 6 and 10 give ND8, ND64 and ND1024, with densities of 0.90, 1.81 and 3.01. Switch the labelling input to ND number and the same figures mean something entirely different: ND3 is only 1.58 stops. The number alone tells you nothing without knowing which system it belongs to, which is the whole reason this page has three options.

Questions

Why is an ND1000 not exactly ten stops?

Because ten stops is a factor of 1,024 rather than 1,000. ND1000 is 9.97 stops, a difference of about three hundredths of a stop, which no sensor will ever show you. Manufacturers round to a tidy number.

Can I meter through the filter?

Through a light one, yes. Through a ten-stop, usually not, because the meter runs out of range and the autofocus stops working. Meter first, then fit the filter and apply the result.

Do stacked filters add or multiply?

The stops add and the ND numbers multiply, which are the same statement. A six-stop with a three-stop is nine stops, or ND64 times ND8, which is ND512.

What about colour casts?

Strong filters often shift colour, usually towards magenta or blue, and the heavier the filter the worse it tends to be. That is a white balance problem rather than an exposure one and the arithmetic here is unaffected.

Does this work with a polariser as well?

A circular polariser costs roughly one and a half to two stops depending on its angle to the light. Add that into the stacked field if you are using one.

For trading shutter against aperture and ISO, see exposure equivalent. For how much of the scene stays sharp there is depth of field, and for exposures long enough that the stars move, the 500 rule.