Update!

This NPF Rule has now been added to the excellent PhotoPills app to get real time shutter speed recommendations as you pan through the sky with your smartphone. Read more about it here: https://www.photopills.com/blog/update-photopills-now-and-avoid-trails-your-milky-way-photos There are screenshots on how to use it down below.

500 Rule

Wide angle lenses let you use longer exposures at night without stars streaking. A frequently used rule of thumb is to divide 500 by your focal length for the maximum number of seconds you can use for an exposure and still get acceptably sharp stars. Sometimes it's called the 600 Rule or the 400 Rule or several other numbers that can be used depending on your sensor size. It’s a relative figure—stars don’t appear to move as fast near the north star, but the further away from Polaris and the closer to the equator you get, the faster the stars appear to move. It's also a very inaccurate rule today as it was designed for 35mm film grain at higher ISOs; current digital sensors far out-resolve grainy film, especially with high-megapixel count, medium format, or printing larger than 20" x 30". It does not take into account pixel density, aperture, or diffraction. However, it is an easy formula to remember and calculate in your head in the field, so it is often used. If you don’t have a 35mm full frame sensor, divide again by the crop factor (1.6 for Canon crop sensor DSLRs, 1.5 for Nikon crop sensor DSLRs, and 2 for most mirrorless cameras). 14mm to 35mm on a full frame sensor is best for Milky Way photography. 50mm and higher usually needs a tracker to avoid streaking at long enough shutter speeds.

Here are some examples:
500 ÷ 14mm on a full frame sensor = 35 seconds
500 ÷ 24mm = 20 seconds
500 ÷ 18mm ÷ 1.6 for a Canon crop sensor = 17 seconds
500 ÷ 50mm ÷ 2 for a mirrorless sensor = 5 seconds

I often subtract another 5 to 10 seconds from these estimates to ensure sharp stars when shooting along the horizon, especially when printing larger than 12" x 18" from a high resolution sensor. For timelapses and star trails a small amount of streaking won’t matter. A web-sized image for social media at 2048px wide won’t matter much either.

NPF Rule

I used to use the 500 Rule (and 450 Rule, 400 Rule, etc.) when I shot with 35mm film and my 12MP Nikon D700. When I upgraded to a 36MP Nikon D810 it just didn’t hold up anymore with 20” x 30” prints and larger. I was still getting streaking at times depending on the area of sky I was looking at or the aperture I used, especially when aligning and stacking. So I set out to find a more accurate formula. After a bit of research I stumbled across Frédéric Michaud’s paper for the Astronomical Society of Le Havre in France that he titled the NPF Rule: https://sahavre.fr/wp/regle-npf-rule/

Here is the “simplified” formula, which uses some averages for latitude, declination, etc.:
(35 x aperture + 30 x pixel pitch) ÷ focal length = shutter speed in seconds.

To figure out the pixel pitch of your camera, divide the sensor’s physical width in millimeters by the number of pixels in width, and multiply by 1000 to measure it in microns. For example, a Nikon D850 is 35.9 x 23.9mm and 8,256 x 5,504 pixels.
35.9 ÷ 8,256 x 1,000 = 4.35 μm (rounding up).

Therefore, a 14mm f/2.8 lens on a 45MP D850 would equal about 16 seconds: (35.9 x 2.8 + 30 x 4.35) ÷ 14 = 16.4979 seconds. Don’t forget your “order of operations” from high school math class for the above formula: solve the multiplication before the addition or you won’t get the correct results!

The 500 Rule would say 500 ÷ 14 = 35.7 seconds, which has significant streaking in the corners on a 45MP camera if you zoom in or print large. You could probably get away with 18-20 seconds though and look acceptably sharp for most uses if you aren’t picky about perfectly round stars.

That's a lot of mental gymnastics in the field, so I made a large spreadsheet (bottom of this article) of common camera models that became quite popular on Fstoppers, PetaPixel, PhotographyLife, etc. It was a pain to keep up to date and to use in the field with a smartphone though, so I contacted the developers of qDslrDashboard, PhotoPills, and PlanIt Pro to see if we could get it added to their wonderful apps.

qDslrDashboard

Below is a screenshot of the NPF Rule in qDslrDashboard when you click the Rule 600 button. Unfortunately, qDslrDashboard does not have an included database of common camera models, so you have to know your sensor size and image pixels to enter when you are in the field.

NPF Rule in PhotoPills

The team behind PhotoPills are good friends and very open to suggestions for new features, so we had a great discussion over several weeks on how to use the augmented reality (AR) feature of PhotoPills to take advantage of the full NPF formula, which takes into account GPS location, compass heading, and declination or angle of the sky you are looking at for real time calculations as you pan through the sky! Here are some screenshots on how to use it...

Go to the Spot Stars "pill". Here you choose your camera model, focal length, and aperture. Above is my Nikon D850 with a 14-24mm f/2.8 for example. The NPF Rule shown here is the simplified rule that uses some averages for latitude & declination, and assumes you are shooting the galactic core or center of the Milky Way. On average, I can shoot 15 second exposures and get sharp stars. For a real time readout using the extended formula for your GPS location, compass heading, and specific area of the sky you are pointing at, click the AR button in the lower left corner and see the next photo.

Here is a real time readout of the extended NPF Rule using your GPS location, compass heading, and pitch/angle. Put the crosshairs on the center of your camera's framing and it will tell you the ideal shutter speed for the entire image, based on the focal length and aperture you chose previously. If you want to check another GPS location, click settings, disable autoupdate, and search for an address or GPS coordinate. Make sure autoupdate is enabled if you want accurate results for your current location. The ability to load the pin's current location in the planner view is coming in a later update.

Notice the shutter speed lengthens near the north celestial pole where star movement is not as noticeable.

Back to the main screen for Spot Stars, the top right icon is set to Default. For most applications this is fine, unless you are printing larger than 24” x 36” or if you are stacking multiple images to reduce noise. In which case, you can make the stars even more pin-sharp by choosing accurate. It will roughly half the suggested shutter speed. I recommend accurate when stacking 10-15 images to get less movement.

Updated on 2017-04-17: added several more camera models and a new column for lens mount type.

This spreadsheet is pretty much obsolete now with the NPF Rule being added to popular apps like qDslrDashboard and PhotoPills. I've left it here on this blog post though for historical record since so many articles link back to it.

Instructions

There are many more camera models in the spreadsheet than the screenshot above. You can sort or filter by brand or model by clicking the drop down arrows for each column (not shown here). By default it is sorted by the Exposure column. Some of the column descriptions are clickable hyperlinks to their source for more information. I'll summarize each column below...

Maximum PDR is Photographic Dynamic Range, typically at base ISO. It's more accurate than the manufacturer's specified claims for real world usage and editing. This gives you an idea of how much highlight recovery or shadow boosting you can get from a RAW file. A higher number is better.

Low Light ISO is the recommended highest ISO to use for the night sky with minimal noise for each camera model. You can go higher, but you'll have to use more aggressive noise reduction techniques in post-production. Some cameras have a better low light ISO, but less dynamic range (Nikon D5 for example). Some cameras have more dynamic range, but not as good a low light ISO (Nikon D810 or Sony a99 as examples). That being said, all three of those cameras are excellent choices for shooting the Milky Way. A few, rare camera sensors are exceptional at both high ISO and dynamic range, such as the Sony a7R II.

Low Light EVmirrors low light ISO performance when comparing cameras, and really isn't all that useful without also taking into account focal length, aperture, and shutter speed for sharp stars, so the Exposure column will probably be of more interest for shooting the night sky.

Read Noise ISO is the highest ISO that is still capturing more photons than amp gain. It is likely to be extremely noisy, but it is useful for stacking many images to reduce noise as you are still capturing light from weak stars. You probably won't use this high an ISO for anything except stacking, and even then you will likely prefer a lower ISO.

ISO invariance (highlighted in red): some sensors are unique in that the read noise ISO is lower than the low light ISO, this means you aren't actually capturing more data at a higher ISO and you can boost the exposure in post-production with pretty much the same results because the lower read noise ISO has more dynamic range. The exposure and histogram will not look correct on the back of the camera, but the data is there in the RAW file. You can also use a higher ISO and reduce the exposure in post-production to hide noise better, but you'll be losing some dynamic range. This is called ISO invariance and there is an excellent article on the topic here: https://photographylife.com/iso-invariance-explained. These special sensors have been marked in red in the read noise ISO column of the spreadsheet.

Sensor width and sensor height are pretty self-explanatory. These are from the manufacturer's specifications.

Pixel width and pixel height (mostly from DxOMark) is the actual sensor resolution before demosaicing the Bayer matrix--not the somewhat smaller image resolution you will see in the RAW files. This makes the calculations for pixel pitch, circle of confusion, and shutter speeds much more accurate. Megapixels will be slighter higher than effective resolution as a result.

Pixel pitch is the camera sensor's physical width in millimeters divided by the number of pixels in width times 1,000 to measure it in microns. It is the density of the camera sensor and the size of a single photosite. 

CoC is the circle of confusion or resolving power of the camera sensor, based on the pixel density. It is the width of two photosites measured in millimeters. More megapixels in the same physical area results in more resolving power and thus a tighter circle of confusion. This is very useful for depth of field calculators when printing large or zooming in for gigapans. Most hyperfocal and depth of field calculators assume a CoC of 0.030mm for 35mm full frame sensors, based on film grain and viewing distance, but today's digital camera sensors are capable of resolving much more. For example, a 50MP Canon 5DS R has a true CoC of 0.008mm if you want critical sharpness when zoomed in to 100%. If you use 0.008mm in your favorite DoF calculator, such as PhotoPills, you will find a much shallower depth of field for any given aperture, and much further hyperfocal distance. In practice, this is really extreme and doubling the true CoC will still give you fantastic results when printing large, much more so than the default 0.030mm for full frame sensors. If you want to know more about depth of field, hyperfocal distances, and circle of confusion, check out this incredible article by the PhotoPills team: http://www.photopills.com/articles/ultimate-guide-depth-field

Diffraction is the aperture at which you start losing sensor resolution on a pixel level, at 100% zoom. Practically speaking, the depth of field gain from a smaller aperture than this value is usually worth the slight loss of sensor resolution unless printing very large or zooming in close for gigapans.

Focal Length and Aperture are the two fields that you will want to change to match your lens. The default values entered here are the widest lenses I could find for that lens mount to give maximum brightness for the Milky Way. It might not be the best aperture for coma though, and stopping down a little will often give you better results. Closing the aperture a full stop will give you about a 1/3 stop increase in shutter speed time, but you'll still be losing 2/3 stop light overall. Longer focal lengths will dramatically lower the shutter speed. Beyond 35mm on a full frame sensor will probably require stacked photos or a tracker.

Shutter is the above-mentioned NPF rule for sharp stars based on sensor size/density, recommended low light ISO, focal length, and aperture. It assumes 550nm as the average wavelength of visible light on the color spectrum and an average declination of 60°. Check out Frédéric Michaud's paper for more information on the math and physics behind the formula: https://sahavre.fr/wp/regle-npf-rule/

Exposure is the light level you are exposing for measured in EV based on the ISO, aperture, and shutter speed. The spreadsheet is sorted by this column by default from the best exposure of the night sky to the dimmest, based on the recommended maximum low light ISO and fastest lens I could find for each camera. Because these are negative EVs you have to think in reverse. -6 to -7 EV is a good range for detailed images of the Milky Way, assuming no light pollution and no moonlight. -8 EV or lower (-9, etc.) will probably be a little over exposed, but you can lower the exposure slider in post-production to hide noise. -5 EV or higher (-4, -3, etc.) will probably be a bit too dark, but you can raise the exposure slider in post-production at the risk of introducing more noise. With an ISO invarient sensor, you shouldn't notice much difference between raising the ISO in camera or the exposure slider in Lightroom / Camera RAW, so you can shoot at the read noise ISO (the ones highlighted in red) for more dynamic range on those camera models instead of the low light ISO, regardless of what the measured exposure says in EV.

Data Sources

Many thanks to the following websites for most of this data:
http://photonstophotos.net
http://www.digicamdb.com
http://www.dxomark.com
https://photographylife.com/iso-invariance-explained
https://photographylife.com/what-is-diffraction-in-photography
http://www.photopills.com/articles/ultimate-guide-depth-field
https://sahavre.fr/wp/regle-npf-rule/

For more information and tips about finding the Milky Way and night photography in general, check out my article on Night Sky Photography:
http://galleries.aaronpriestphoto.com/Articles/Night-Sky-Photography

Thanks for reading and feel free to share this page with others! Happy shooting!!!