ND Filter Exposure Calculator (Long Exposure)
Shutter speed with a neutral density filter from the speed without it and the filter's strength in stops, with the ND factor and optical density.
Results
The dashed line marks the value you entered.
What this tool does
Each stop halves the light, so each stop doubles the exposure time: a 10-stop filter (sold as ND1000, density 3.0) turns 1/125 s into about 8 seconds, enough to smooth water and blur clouds. Filters are labelled in three ways — stops, the ND factor (2 to the power of the stops) and the optical density (0.3 per stop) — and the results give all three. 1/125 s is 0.008 s. Very strong filters often let some infrared through and many are not exactly the nominal strength, so check the histogram and adjust.
Formula
t = t₀ × 2^stops · ND factor = 2^stops · optical density = stops × log₁₀ 2
Variables
| Symbol | Meaning | Unit |
|---|---|---|
t0 | Shutter speed without the filter | s |
st | Filter strength in stops | — |
T | Shutter speed with the filter | s |
TM | Shutter speed in minutes | min |
NF | Filter factor (ND number) | × |
OD | Optical density | — |
TR | Light let through | % |
Worked example
- Shutter speed without the filter0.008 s
- Filter strength in stops10
- Shutter speed with the filter8.19 s
- Shutter speed in minutes0.14 min
- Filter factor (ND number)1024 ×
- Optical density3.01
- Light let through0.0977 %
Limitations
- The default values are typical reference figures, not measurements of your situation. Replace them with your own data whenever you have it.
- The calculation runs at full precision and only the display is rounded. If you copy an intermediate value and retype it, small differences can appear.