FORMULAS · ASSUMPTIONS · PRIMARY REFERENCES
The number needs
a notation.
NDtime computes ideal shutter-duration changes from entered filter attenuation. You supply the unfiltered reference duration and retain the same aperture, ISO and scene illumination.
Three exact mathematical definitions
| Selected input | Time factor F | Example |
|---|---|---|
| Stops s | F = 2s | 3 stops → ×8 |
| Optical density D | F = 10D | OD 3.0 → ×1000 |
| Filter factor F | The entered factor | Factor 8 → ×8 |
For each filter, stops = log₂(F), optical density = log₁₀(F), and calculated light transmission is 100/F percent. Stack ideal uniform filters by multiplying their factors; equivalently, add their stops or add their optical densities. The filtered duration is the reference duration multiplied by the combined factor.
Why “ND” alone is ambiguous
Manufacturer labels use different scales and rounded equivalences. HOYA’s ND explanation describes ND2, ND4 and ND8 as factor-style numbers corresponding to one, two and three stops. LEE’s ProGlass IRND instructions show density-style labels such as 0.6ND alongside nominal stop labels.
The formulas distinguish exact values from those nominal labels. Exactly 2 stops has OD log₁₀(4) ≈ 0.602060. Entered OD 0.6 has factor ≈ 3.981072 and loss ≈ 1.993157 stops. Do not treat a printed “ND8” as eight stops, or assume a decimal label means stops. Check your filter’s documentation and choose the stated scale.
Worked example: exactly 10 stops
Start at 1/125 second, which is 0.008 second. Enter 10 in Stops. The factor is 2¹⁰ = 1024 and the duration is 0.008 × 1024 = 8.192 seconds.
For the same starting time, literal Factor 1000 gives 8 seconds. OD 3.0 also gives 8 seconds. These inputs differ by about 0.034216 stops; the tool retains that difference rather than substituting a rounded product name.
Worked example: two stacked filters
With the same 1/125-second reference, enter one filter at 6 stops and a second at 3 stops. Their factors are 64 and 8. The combined factor is 512, the total loss is 9 stops, and the ideal duration is 4.096 seconds. A 10-stop filter stacked with a 3-stop filter instead gives 65.536 seconds, or 1 minute 5.536 seconds.
Notation changes preserve the entered attenuation
Changing a row from Stops to OD or Factor converts its displayed value. The original attenuation remains cached, so converting 10 stops to OD and back does not repeatedly round it into a different exposure. Editing the displayed number deliberately establishes a new entered basis. The results table and text report retain that basis.
Limits that matter in practice
This model assumes uniform attenuation across the frame, independent stacked factors and an accurate starting exposure. It does not select a filter, aperture, ISO, lens or desired motion effect. It does not estimate variable-filter calibration, reflections, vignetting, colour shifts, exposure changes during the shot, camera timing limits or noise-reduction processing.
LEE’s Stopper guide notes changing illumination and film reciprocity effects. No film reciprocity correction is included here; use the specific film manufacturer’s data when it applies. A generic extra multiplier is not a substitute for that data.
The tool accepts one to four active filters, each from factor1 to factor2⁴⁰, a starting duration from 0.000000001 to 86,400 seconds, and a resulting duration up to 7 days. These are software bounds, not photographic recommendations. Logarithms and non-integer powers use browser floating-point arithmetic. Values are rounded for display; manufacturer exposure cards can also round to convenient camera settings.