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If you stack two 3-stop neutral density filters, does it reduce the exposure by 6 stops or 9 stops?

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It's six.

Remember, the stops are already logarithmic. That is, a 3-stop reduction (as from a 3-stop ND filter) is a 2³× loss of light — ¹⁄₈ of the light gets through. A one stop filter halves light, since 2¹ is just 2 (→ ¹⁄₂), and two stop filter is 2² (→ ¹⁄₄ the light). When you stack them together, you're adding the exponents, so 2³ stacked with 2³ is 2⁶ — or ¹⁄₆₄th the light. That's the same as thinking "three stops is one over 2³, or ¹⁄₈, and ¹⁄₈ × ¹⁄₈ = ¹⁄₆₄ — which is one over 2⁶".

But, fortunately (and in fact partly why it's done that way), you don't have to remember all this. Just remember that 2³ × 2³ = 2⁶ — or, 3 stops plus 3 stops is 6 stops.

Of course, this is just the math. In the real world, there may be other practical effects, like vignetting in the corners (due to the increased thickness) or color casts — you're adding more layers for the light to go through, and that takes a toll on image quality. See the comments below.

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  • \$\begingroup\$ +1 but you could have summed up as 6! \$\endgroup\$
    – Joanne C
    Commented Apr 2, 2011 at 0:28
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    \$\begingroup\$ @mattdm - The kernel of your answer always comes in the last sentence or two. Maybe a little bold highlighting or people who skim for the short version? \$\endgroup\$
    – Sean
    Commented Apr 2, 2011 at 0:32
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    \$\begingroup\$ But the site doesn't take one-character answers. :) \$\endgroup\$
    – mattdm
    Commented Apr 2, 2011 at 0:45
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    \$\begingroup\$ You forgot to explain the law of stackability failure ;) Two 3-stop ND filters = 6-stops, but three 3-stop filters equals 9-stops in the center and 10-stops along the edges due to vignetting. \$\endgroup\$
    – Itai
    Commented Apr 2, 2011 at 1:35
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    \$\begingroup\$ Be careful though. Cokin ND filters give a colour cast when you stack them, as I found out to my cost! \$\endgroup\$
    – user456
    Commented Apr 2, 2011 at 16:40
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In addition to @mattdm's answer - the result of stacking ND filters can also be vignetting.

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