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

Michael C
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rmart
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2 Answers2

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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.

mattdm
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  • +1 but you could have summed up as 6! – Joanne C Apr 02 '11 at 00:28
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    @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? – Sean Apr 02 '11 at 00:32
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    But the site doesn't take one-character answers. :) – mattdm Apr 02 '11 at 00:45
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    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. – Itai Apr 02 '11 at 01:35
  • Excellent! To quote Mr. Burns. – Joanne C Apr 02 '11 at 01:35
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    Be careful though. Cokin ND filters give a colour cast when you stack them, as I found out to my cost! –  Apr 02 '11 at 16:40
  • This is all very helpful, thank you all! And specifically to Nick Miners, this was actually in reference to some cheap Cokin filters I picked up just to play around with, so that's good to know! – rmart Apr 04 '11 at 04:09
  • Bring back high school math+physics all over again, good explanation! – Bill Jul 31 '12 at 15:55
  • 2³ + 2³ = 16. which is 2^4. Your math is wrong. if you meant 2^3 x 2^3 then it is 2^6. –  Jun 24 '13 at 18:25
  • @Ken — fixed. I was improperly using "+" to mean the colloquial "in combination with", and should have used a multiplication sign when writing it in equation form. – mattdm Aug 14 '13 at 02:31
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In addition to @mattdm's answer - the result of stacking ND filters can also be vignetting.

ysap
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