# formula for camera megapixels to print size?

Discussion in 'Digital Darkroom' started by megan_stone, Sep 25, 2009.

1. ### megan_stone

i am aware that many people dont abide by such rules and one can push print size at times.
but i have been told that there is a formula to calculate what an appropriate print size is according to a camera's megapixels.
much thanks

2. ### Matt Laur

Being conservative (erring on the side of a higher quality print), assume 300 pixels per inch.

So, a camera sensor that has, say, 3000 pixels across would produce a print that is 10 inches across in that same dimension.

Rather than thinking in terms of megapixels, think in terms of pixel dimensions. The file is (natively) some number of pixels wide, and some number of pixels tall. Just divide those numbers by the pixels-per-inch of the printing device/service, and you'll knw how many inches you can go with before having to upsize the image (or have the printing process do it for you).

3. ### matthew_newton

A 5.3 mega pixel camera is approx. 1889x2835 pixels. This enables about a 6x9 print going with slightly more then 300 pixels per inch for the final print size (overly conservative). For every quadrupling of the pixel count you can double the print size. So to go up to 12x18 with the same very conservative DPI of the final print you'd need a 21.2 megapixel camera. To get a 24x36 you'd nee 82.8 megapixel. All it is is the square of the increase in the dimensions (IE if you went up 50% in size (1.5) then you'd need 2.25 times as many pixels).
Of course this is also for the same viewing area of the print. I don't think I'd be viewing a 24x36 print at the same distance I would a 6x9...so in reality for the 24x36 I'd probably only need 4-6 times as many pixels, not 16 times as many (4 times 4).
On a little looser, but still plenty acceptable DPI count (call it 240) that 5.3 megapixel print could also be printed at about 8x12 and still look just fine unless you were eyeballing it really close.

4. ### howard_m

there isn't just the x/y = 300 calculation that Matt refers to but also that there no one is going to be putting their nose up against a huge print. the viewer is going to be standing back and the larger the print, the further back in general. Then there is the issue of human vision acuity.
At the end of the day, the 300ppi is a nice target but in most cases, you can be down to 1/2 that number, in the mid-100's and not notice it.

5. ### luis_g

http://www.bythom.com/printsizes.htm

6. ### scott_ferris

Megan,
Like so many of these things it is very subjective. But 300 dpi has now come to be accepted as very very conservative. Different printers and cameras and the multitude of combinations all mean people end up with their own preferences but 240 is more than good enough even for most high quality applications. Also printers have a large effect on it all, they all convert a comparatively small number (pixels) into a much higher number (the huge number of print head jet blasts).
Anyway after that butt covering waffle, I, and many others ( third paragraph, http://wyofoto.com/EOS_IQ_shootout_2008/EOS_shootout_2008.html ), have never had anybody tell the difference between a 240 dpi and a 300dpi print.
So my 4.1 mp camera at 2480x1646 pixels will print out natively, perfectly, at 10"x7" realistically without resizing just sending to the printer to "fill" it does an 11x8.5, letter size.
My 15 mp camera at 4416x3312 pixels will print out natively at 18"x14".
My 21 mp camera at 5624x3736 pixels will print out natively at 24"x 16".
If you crunch these numbers you will see that there is close to a constant, if you take your print in square inches (10"x7"=70 square inches) and divide by the mp (4.2) you get 17 ish. So between 17 and 18 square inches per mp. If you want a known sized print then just divide the prints square inches by 17 and that will give you the mp you need.
An example cos that all seemed long winded
Print size wanted 12"x18"
12"x18" = 216 square inches divide 216 by 17 = 12.7 so a 13mp camera
Hope this makes sense.

7. ### ben_goren

Scott,
I’m nearly entirely in agreement with you as far as resolution goes; there’s just one obscure exception I’d like to point out. And that’s that, for art reproduction, the difference between 240 and 300 ppi is discernible, and so is the difference between 300 ppi and 600 ppi. The reason is that, as photographers, we can use post-processing techniques to enhance acutance, but art reproduction requires that you have the actual fine details visible rather than a facsimile thereof.
Whether or not you need 240 or 300 or 600 or whatever to reproduce a particular work depends (as usual) on the work, the demands of the artist, and all the rest of the usual caveats. Fortunately, paintings generally don’t move all that fast, so you have the (tedious) option of stitching a panorama by shifting the work around under the camera.
Or, of course, you could spend stupid amounts of money on a scanning back, etc.
Cheers,
b&

8. ### tallplumphotography

Though I don't use SmugMug to print, I found this to be a helpful guideline: http://www.smugmug.com/help/print-quality
Keep in mind that those are calculated using fairly high-quality images in the first place - if you're using old, junky overly compressed files, the number of pixels isn't going to matter that much.

9. ### kelly_flanigan|1

In printing for the public my take is that folks who worry about megapixels versus print size create the VERY worst inputs. Their mindset is involved in what does not often matter; thus part of their brainpower is off worrying about nonsense; instead of a using a powerfull image.

Unless viewing distance is known and purpose; there is no answer to the weekly "how large can I enlarge" questions.
It will be asked until end of time.
It is like asking how long a pice of string or piece of rope needs to be.

A VGA image is good enough for a 12 by 48 foot billboard; ie overkill too.

For a super detailed map here we sometimes require an image that is at the print level at 360 to 400 ppi too.

The human eye only resolves a certain arc angle.
In a pro print there is an actual client; an actual purpose for the image.
Maybe it is a hockey dasher board where the viewing distance is 85 feet awayas a typical best case closest distance. Folks may want 300 ppi at 1 foot to be sharp; that is like 30 ppi at 10 feet; 3.5 ppi at 85 feet. Thus a 3 foot high dasher board only requires 36 inches times 3.5 ppi or 126 pixels. If it is 10 feet long then one has 120 inches times 3.5 or 420 pixels. A cell cam or Barbie cam bubble packs image is overkill for a 3x10 foot hoclkey dasher board. BUT a more newbie or amatuer dasher board client will "get the 300 ppi/dpi" requirement etched into their brains; and thus totally focus on this balls to the wall super detailed image; and DEMAND we learn something. One can got to the rinks and spot the newbies images; dull; lifeless with zero soul; BUT THEY LOOK SHARP IF ONE IS 1 FOOT AWAY!. Part of the cost of digital printing for the public is handholding; hearing lectures as new folks jump on the digital bandwagon. Its abit funny since I first printed some hockey dasher boards/vinyls 20 years ago with a pen plotter driven by a 286.

Consider what matters; ie viewing distance.

An image that is say printed at 300 pixels per inch viewed at 1 foot is considered as sharp to many.

Thus this equates to:

An image that is say printed at 100 pixels per inch viewed at 3 feet

An image that is say printed at 30 pixels per inch viewed at 10 feet

An image that is say printed at 10 pixels per inch viewed at 30 feet

An image that is say printed at 3 pixels per inch viewed at 100 feet

An image that is say printed at 1 pixels per inch viewed at 300 feet
Thus a billboard that on an interstate highway that is best case 300 feet away only requires a 1 pixel per inche image. If it is say a giant 12 by 48 foot billboard; that image needs to be only 144 by 576 pixels; one 13th a megapixel. ie barbie cam; ie way less than a cellphones image of 4 years ago. If one gets a flat tire right by the billboard and one has pilots eyes the image still is sharp; since it is 300 feet away.
Amatuers will always argue that one could in theory go over the barbwire fence; dodge some mad bulls; climb up the billboards tower and see the flaws of a 1 pixel per inch image. Becaise amateurs cannot *box in* or define *viewing distance* or a print/poster/etc; overkill is often the preached dogma. One might have a billboard that is 300 feet away best case; that on has to trespass, risk ones life to see its flaws and folks will still preach 300 dpi/ppi; off by a factor of 300 to one.

A photo or poster of billboards requirement for details is like as scale model in a movie; it needs to be good enough for the job; but not overly detailed to flush money down the drain with added costs and labor.
Many folks prescribe overkill; since it is hard to box in the viewing distance; it involves actual thought.
Thus it is their house they are selling; in like matter 300 dpi/ppi printing is like cutting each blade of grass with sissor and a micrometer; a prospective house buyer will inspect the yard at 1 foot for flaws.

Understanding how close one needs to be as to requirements is fundamental; whether one is making coffee; lunch or an image for a client.
Preaching 300 dpi/ppi is like measuring coffee with a Mettler balance; it does not hurt; it just wastes time and money.
Consider what matters; ie viewing distance.

10. ### megan_stone

thank you everyone - that was helpful.
i print at 360dpi on my Epson 3800 - as i've been told thats the "magic" number... im now reading 300 and in some cases even less.
thoughts?

11. ### kelly_flanigan|1

Once one has a viewing distance defined; one has a required print pixel per inch boxed in; ie defined.
Once one has the target ppi defined and print size; one multiplies that figures the number of pixels for each side.

Thus if one has say a 3x4 foot poster that one CANNOT get closer than 6 feet; all oen has to do is turn the crank to figure the image size. With a 300 ppi at 1 foot; one gets 50 ppi at 6 feet; ie feet times ppi equals 300. A 3x4 foot image is 36x48 inches; thus the requirements are 36x50 by 48x50 pixels; ie 1800 by 2400 pixels; ie a tad over 4 megapixels. One might have this warning poster 6 feet away from a river of molten lava and some folks will argue that 50 ppi is not enough; one could walk across lava; or use a set of binos to discover the poster's flaws.

If one has a 16x20" print that is to be viewed at 1 foot away; we need more pixels than the lava warning poster. The 16x20 print needs say 300 ppi; ie 16x300 by 20x300 pixels; (if ones criteria is 300) thus the *pixelage* is 4800 by 6000 pixels; it alot higher ie about 28 megapixels.

One might be printing a super detailed city wall map that is 3x4 feet that requires a 400 ppi image; now one has 36x400 by 48x400 pixels; ie 250 to 300 megapixel image; easy to get from our 600 dpi 36" wide RGB scanner.

One might have some 8x10 " photos to print for ones grandmother; whos eyes really cannot see any more details beyond say 150 pixels per inch in a print. She might like a 8x10 inch print printed at 150 ppi versus the same image printed at 300 ppi and a 4x5 print; since the 8x10 print shows more details with her eyesight. Thus we have the SAME number of pixels spread across 4 times the area; to make them easier to see; ie a greater arc angle.
At some point the printer is the limit; besides one's eyes. If one prints a detailed image say at 200, 250, 300, 350, 400, 450, 500, 550 etc pixel per inch to a printer; the details get *lost*. It depends on the printer; the paper type; the image type too. Printing on canvas or tshirt or bathtowel will not *support* alot of ppi; nor will misaligned print heads either.
Run some tests!

12. ### kelly_flanigan|1

One might have a client that wants the print on some very coarse canvas product that can only support say 100 to 120 ppi; before all details purge into the canvas. Here if one say sends the printer a detailed 300 pixel per inch image; it will look the same as it is was downsized to say 100 ppi; thus one has one nineth the megapixels required; since the coarse print material low passes the details; ie details are lost in the coarseness of the canvas.
Think super fine writting on a fluffy bath towel; it just does not work.

Thus if one has a 2000 by 3000 pixel image and one has this coarse canvas; one could make a print that is 20 by 30 inches at 100 ppi; since that is all the printer will support. 100 ppi is good to 3 feet; if one could box in the closest distance as only 6 feet; one could make the canvas print bigger; ie 40 by 60 inches; since now only 50 ppi is required at 6 feet.

The general public has a hard time with boxing in what the closest viewing distance is with prints and posters; thus there is a huge amount of total confusion of "how big can I enlarge" questions.

Having a bigger piece of film or more megapixels allows for cropping more; or future image usages at closer distances too.

13. ### indraneel

Signac, Seurat and Van Gogh's works are displayed in large halls for a reason. Unlike digital sensors, the cost of paints has not gone down appreciably in the last centuries. That is also why most photo printers also give a choice of dithering and dpi based on whether one is printing a transparency or banner. Coarse dithering with low dpi benefits little from high ppi.

14. ### lalon_karim

Don't forget that acceptable print size varies with ISO also. More noise and noise reduction -> small acceptable print size. According to imaging-resource (http://www.imaging-resource.com/PRODS/AA900/AA900IMAGING.HTM), u can print sharp 20x30 print at ISO 100 and 200 from Sony Alpha 900 (25 MPixels). ISO 400 and 800s are good for 13 x 19 inch prints. ISO 1600 and 3200s are good for 5x7 inch prints only!

15. ### dan_south

Nobody wants to hear this - because everybody loves numbers and everyone things that more is better - but a lot depends on (a) the sensor and (b) the image processing software inside the camera. I defy anyone to compare a print from a 12 MP D2x with a 12 MP D3 and tell me that they look the same. The D3 image will have a lot more apparent detail than the D2x image, even though both sensors have the same number of pixels.
For the same reason I would be willing to bet that a 22 MP Phase One sensor will outperform a 21 MP Canon sensor or a 24 MP Nikon or Sony sensor (although I haven't made this comparison myself).
So, no, there is no formula that translates the number of pixels on a sensor to the maximum print size of its output. There are too many variables in digital sensor design. Sensor performance cannot be expressed as a simple function of the number of pixels that it contains (although every gearhead on the planet seems to think so).

16. ### lalon_karim

... and in contrast: Nikon D90 (12 MPixels) is good for "good 20x30 inch prints, excellent 16x20 inch ones. ISO 3,200 images are surprisingly good at 8x10, even better at 5x7" (http://www.imaging-resource.com/PRODS/D90/D90IMAGING.HTM). So it seems there is a no single formula for relationship between print size and megapixel.
When viewing distance is concerend I personally like the assumption that minimum viewing distance = diagonal length of the print (or may be 1.25x of diagonal length of the print). U need to stay at least in this distance to see the entire print at a glance.

17. ### sebastianmoran

I stumbled on a very interesting site that's pushing the limits... The Gigapxl Project built special cameras and processes to produce very large print images of 1-4 gigapixels.
Why is this relevant here: They examined closely your question, print size and megapixels. They conclude, FWIW, that at 8 square inches per megapixel, you have a print that will look really good even at very close examination by the human eye.
This means 3 megapixels for a 4x6, 12 megapixels for 8x12, and 10 megapixels for 8x10. This is for a print that will stand very close examination, held as close as you want.
That's a tough standard for large prints; all of us have produced great prints with fewer pixels. But I thought this an interesting starting point.
This isn't about pixel-peeping. It's about what happens for the viewer if the image still has full detail as you move up very close.
To test this myself, I created a 100 MPx image of a friend's home, stitching twenty d200 images with PTGui, printed at 20x50 inches (10 square inches per megapixel, not 8 but close). The large print has an amazing feel. Viewing the print, moving in closer, something happens I don't find in most photographic prints... start by viewing the whole image, then pull it as close as your want, you feel you can walk right into the image. Shift back and forth between close viewing and full image. Viewing the image, pulling it closer, the usual breakdown in quality that separates image from object in a large print just never happens. The scene is fully there, as close as you want to look. This is, of course, hard to describe and hard to illustrate. But, my viewing experience convinces me that you can never have too many pixels for an image intended to convey detail, texture, and substance.
Based on this, I agree with the notion of 8 square inches per megapixel for a print that will stand very close inspection.

18. ### michael_burrows|1

Open it in photoshop, simple

19. ### wildforlight

I get great 30 inch plus prints off of 6 Mega pixels. Sometimes 36 inches.
10-12 and up to 21 Mega pixels I get prints up to 70-100 inches.

20. ### lalon_karim

And sharpness of the lens used is another variable too. If a sharp lens is used, u can print larger than from the same camera using a not-so-sharp lens.

21. ### KenPapai

"It is like asking how long a pice of string or piece of rope needs to be."
The question CANNOT be answered -- in fact, it's a naive question to even ask -- unless you add constraints and then ask. And if you don't even know the constraints you should be in the Beginners forum.

22. ### jacopo_brembati

This question is periodically rised.The answer is always the same.
1 - megapixel are not a good starting point, as Matt Laur said, width and height (number of pixels) are the numbers you have to condider
2 - you have to know the PPI value of your printer driver (pay attention PPI is not a single value, it may change depending on printer settings), or ask for this value to the printing lab
3 - printer driver resamples to the PPI value
4 - printer resampling is "nearest neighbour " (replication in upsampling,decimation in downsampling), fast but crude algorithm
5 - replication/decimation is better if you send a multiple/submultiple of the right PPI value, as pixels are replicated/decimated in a uniform way
6 - the view distance is important. There is not any correlation between your image size and the DPI (PPI and DPI are fixed depending on printer settings). Artifacts are more visible from short distance.
7 - downsizing an image, produces aliasing artifacts. For strong reduction the image must be filtered (low-pass filter) before resampling.
On www.photoresampling.com you can find an article on PPI/DPI.