ND Filter Calculator
Exposure time, stops, and light reduction for a neutral density filter.
What it does
A neutral density filter reduces the amount of light reaching the sensor without changing the color of the scene. Photographers use one to slow the shutter for motion blur, to open the aperture in bright light, or to keep a video shutter angle in range. The filter is rated by optical density, a logarithmic measure of how much light it blocks.
Density and stops are related but not the same number. One stop is a factor of two, which is a density of about 0.301. Two stops are a factor of four, or 0.602. Three stops are a factor of eight, or 0.903. A filter marked ND8 passes one eighth of the light, so it is a 3-stop filter with a density near 0.9. A filter marked ND1000 is a 10-stop filter with a density of 3.0.
The new exposure time is the base shutter speed multiplied by the exposure factor. If the base shutter is 1/250 second and the filter is 0.9 density, the factor is about 7.9, so the exact time is about 0.032 second. The nearest common camera setting is 1/30 second, which is a little brighter than the exact value. For a 10-stop filter, the same base shutter becomes 4 seconds.
The default example uses a 0.9 density filter and a 1/250 second base shutter. It returns 1/30 second on the camera, 0.032 second exact, 3 stops, 12.6 percent transmission, and a 7.9x factor. The exact time is the one to use with a timer or a manual exposure app; the nearest setting is the one the camera dial can actually select.
Long exposures add their own problems. The camera may need a dark frame to subtract sensor noise, the battery may drain, and the tripod may move. Very dark filters can also shift color, especially variable ND filters, and cheap filters may not be truly neutral. For solar photography, use a certified solar filter, not a photographic ND filter.
How to use
- Find the optical density printed on the filter. If the filter only shows an ND number, convert it or look up the density.
- Meter the scene without the filter and enter that shutter speed. Use a fraction such as 1/250 or a whole number such as 2.
- Enter the density, not the stop count. A 3-stop filter is about 0.9 density.
- Read the exact time and the nearest camera setting. Use manual mode so the meter does not re-adjust for the dark filter.
- For times longer than 1 second, use a remote release or the camera timer and add a small allowance for shutter lag.
- Check the histogram and adjust with the aperture or ISO if the nearest setting is not close enough.
Formula
- density
- Optical density of the filter, often printed as 0.3, 0.6, 0.9, or 3.0.
- base shutter
- Correct shutter speed without the filter, in seconds or a fraction of a second.
- exposure factor
- How many times longer the exposure must be with the filter.
- stops
- Light reduction in photographic stops; one stop is a factor of two.
- transmittance
- Percentage of visible light that passes through the filter.
The density scale is base 10, while stops are base 2. That is why 0.30103, the base-10 logarithm of 2, appears in the stop conversion. A density of 0.3 is one stop for practical photography, even though the exact value is 0.30103. Stacking filters adds density, so a 0.6 and a 0.9 together act like 1.5, or about 5 stops. The formula assumes the filter is truly neutral across the visible spectrum and that the base shutter is correct. It does not correct for reciprocity failure, which affects some film stocks, or for the camera's shutter efficiency at very short times.
Worked example
Example: 0.9 density filter at 1/250 second
A 3-stop ND filter has an optical density of 0.9. The correctly exposed shutter speed without the filter is 1/250 second.
- Exposure factor = 10^0.9 = 7.94.
- Exact time = 1/250 x 7.94 = 0.0318 second, or about 0.032 second.
- Stops = 0.9 / 0.30103 = 2.99, which rounds to 3 stops.
- Transmittance = 10^(-0.9) x 100 = 12.6 percent.
- The nearest common camera setting is 1/30 second.
- 1/30 is slightly brighter than 0.032 second, so the image may be a fraction of a stop overexposed. Close down the aperture slightly or use a timer for the exact time.
Reference table
| Density | Stops | Transmittance | Factor | New shutter |
|---|---|---|---|---|
| 0.3 | 1 | 50.1% | 2x | 1/125 s |
| 0.6 | 2 | 25.1% | 4x | 1/60 s |
| 0.9 | 3 | 12.6% | 7.9x | 1/30 s |
| 1.2 | 4 | 6.3% | 15.8x | 1/15 s |
| 1.8 | 6 | 1.6% | 63.1x | 1/4 s |
| 3.0 | 10 | 0.1% | 1000x | 4 s |
Limits
- Assumes the filter is neutral across the visible spectrum. Real filters can shift color.
- Does not correct for reciprocity failure in film or for shutter timing errors at very short speeds.
- The nearest camera setting is a standard shutter speed, not the exact calculated time.
- Not a solar filter. Never look at the sun through a photographic ND filter unless it is certified for solar viewing.
Common mistakes
- Entering the ND number, such as 8 or 1000, instead of the optical density.
- Using the nearest camera setting when the exact time is needed for a critical exposure.
- Forgetting to switch the camera to manual mode, so the meter compensates for the filter.
- Stacking filters and adding their ND numbers instead of adding their densities.
- Ignoring color cast from a variable ND filter or a cheap resin filter.
- Using a photographic ND filter for solar viewing.
Try it yourself
Quick checks. Answers sit tucked under each question.
A 0.6 density filter is used at 1/500 second. What is the new shutter?
The factor is 4, so 1/500 x 4 = 1/125 second. The filter is 2 stops.
A 1.8 density filter is used at 1/60 second. What is the nearest camera setting?
The factor is 63.1, so the exact time is 1.05 seconds. The nearest common setting is 1 second.
A 3.0 density filter is used at 1/125 second. What is the exact time?
The factor is 1000, so 1/125 x 1000 = 8 seconds.
Questions
What is the difference between ND8 and 0.9 density?
They describe the same 3-stop filter. ND8 means the filter passes one eighth of the light. Density 0.9 is the logarithmic rating, and 0.9 / 0.301 is about 3 stops.
How many stops is a 10-stop ND filter?
Ten stops, which is a density of 3.0 and a factor of 1000. An ND1000 label also means 10 stops.
Can I stack two ND filters?
Yes. Add their densities, not their stop counts or ND numbers. A 0.6 and a 0.9 stack to 1.5 density, which is about 5 stops.
Why is my long exposure brighter than expected?
The nearest camera setting may be brighter than the exact time, or the base shutter may have been measured with a different meter mode. Use the exact time and check the histogram.
Do ND filters change the color?
A good neutral filter should not, but cheap resin and variable ND filters often add a color cast. A gray card or a custom white balance can help.
Can I use an ND filter to photograph the sun?
No. Photographic ND filters are not certified for solar viewing and can fail under intense heat. Use a dedicated solar filter that covers the front of the lens.
Sources
- Kodak: Wratten 2 Optical Filters, Neutral Density No. 96
- Florida State University: Molecular Expressions, Filters for Color Photomicrography