5/30/2016 - 6:17 PM

Large format resolution

For wall sized graphics and large banners (e.g 3m x 5m), what is an acceptable PPI/DPI for print.
Here's definitions, so we know what we're talking about.

DPI = Dots per inch = units used to measure the resolution of a printer
LPI = Lines per inch = The offset printing 'lines' or dots per inch in a halftone or line screen.
PPI = Pixels per inch = the number of pixels per inch in screen/scanner file terms.
Now you said "As i understand it 300 DPI is the typical for 'small' artworks (esp. for clean text resolution)" -- here you're confusing DPI with PPI (often done.) Raster artwork for print is generally scanned at 300 PPI. Why? Because most raster artwork is printed with CYMK processes at a maximum (generally) of 150 LPI. The rule of thumb is that we need 1.5 to 2 times the LPI in PPI to get acceptable results.

Why are most things printed at 133 or 150 LPI? Because at reading distance for CMYK printing the dots aren't generally discernible. Because of high-speed printing and cheaper paper/printing of newspapers, they are often as low as 85 LPI, so you can see the individual dots easily on the funny pages.

So your question can be distilled down to: what is the minimum LPI halftone screen I need so that it's not distracting at the distance the poster will be viewed? I did a little searching, and actually found a research paper on this subject. The subject was black and white printing, but since colour halftone dot patterns should even be less noticeable, I think the advice can be extrapolated.

Here's the chart:

Distance              Present Study  
20 feet / 6 meters    greater than 10 LPI    
18 feet / 5.5 m       18.75 LPI or greater   
16 feet / 4.9 m       18.75 LPI or greater   
14 feet / 4.3 m       37.5 LPI or greater    
12 feet / 3.7 m       37.5 LPI or greater    
10 feet / 3 meters    50 LPI or greater  
8 feet  / 2.4 m       65 LPI or greater  
6 feet  / 1.8 m       85 LPI or greater  
4 feet  / 1.2 m      100 LPI or greater  
2 feet  / 0.6 m      133 LPI or greater  
1 foot  / 0.3 m      150 LPI or greater  
6 inches / 15 cm     150 LPI or greater
Presumably, for a banner 3m x 5m, you'd be standing at a minimum of, say, 10 feet. (Just eyeballing the wall here.) So, by this table, you'll need 50 LPI minimum. That would mean your raster graphics should be about 100 PPI, or 75 PPI at 12-14 feet. Considering that and the fact that 2x LPI is pretty conservative for reproducing fidelity (often 1.5xLPI is "enough"), this agrees with @e100's advice of 75 PPI being acceptable.

down vote
I think Jan Steinman was close with his angular explanation. The DPI table is good as well but in the end it all comes down to pixels not DPI for photographic images.

Forget DPI, a good rule of thumb is that across your field of view your eye can not see more than 8,000 pixels. Therefore you should not create a bitmap image of more than 8,000 pixels across. If those 8,000 pixels are across 100 inches then your net DPI will be about 80 DPI (8,000 / 100).

If those same 8,000 pixels are across 20 inches you will get 400 dpi (8,000 / 20). An image which is only 20 inches wide will be viewed from closer up so it needs to be a higher DPI. If you were to stretch those 8,000 pixels to an 8,000 inch wide image you would only get 1 DPI but to view that image you would be standing a long way away and you would still not be able to see the pixels.

Use the 8000 pixel max rule and you will not go wrong. The only case where this rule breaks down is if the image is intended to be viewed more than one field of view wide like a long poster going up an escalator.

Learn Photography

Home|About|Privacy, Etc.

Ask Jim|

Printing >
Which Resolution? > Long Answer >
1 - Print Size & Viewing Distance
The pixel dimensions of your photograph, such as 3000 x 2000, don't give it a size.

The pixel dimensions describe only how many pixels there are in your photograph.

If we only know the pixel dimensions, we don't know how large each pixel is.

Resolution is the number of pixels per inch (ppi).

When you enter a resolution figure, you're giving a size to the pixels of your photograph.

For example, a resolution of 300 pixels per inch produces small pixels.

A resolution of 72 pixels per inch produces larger pixels.

If you enter a resolution that's too low, the pixels will become visible.

If you enter a resolution that's unnecessarily high, your eyes will not see any improvement in the print, and it will take longer to print.

What's the best resolution for your prints?

Go to the Printing & PPI Flow Chart for the quick answer.

For the detailed answer, read on.

Six Factors
The best resolution for a print depends largely on six factors.

The first factor is the most important.

Factor #1 - Print Size & Viewing Distance
The best resolution is determined by considering the print size and print viewing distance.

Smaller prints are viewed from closer distances.

Therefore, higher resolutions are needed for smaller prints.

Larger prints are viewed from further away.

Therefore, high resolutions are not needed larger prints.

So, as print size increases, less resolution is needed.

Example #1
The resolution of a billboard-sized photograph is often only 10 to 20 ppi.

The resolution doesn't need to be higher because the viewer is so far away from the photograph.

Example #2
As you move away from your monitor, the lower-resolution versions of the above photograph, below, gradually become as sharp as the original.

The photograph has been cropped to make it easier to fit on your screen.

36 ppi

Uncropped Print Size = 55" x 83"

Typical Viewing Distance = 12.4'

When you're 12.4 feet from your monitor, the bicycle in the above photograph will appear to be sharp.

72 ppi

Uncropped Print Size = 28" x 42"

Typical Viewing Distance = 6.3'

150 ppi

Uncropped Print Size = 13" x 20"

Typical Viewing Distance = 3'

Determining Print Viewing Distance
Harald Johnson, in Mastering Digital Printing, cites a formula by Joe Butts for determining viewing distance.

Viewing Distance = 1.5 x Diagonal of the Print

Some photographers use the less stringent multiplier of 2 instead of 1.5.

Here are the viewing distances for common print sizes, with normal lighting, with the resolution needed for a print with acceptable quality.

If the viewing distance is expected to be closer than the figures below, or if the viewing conditions are optimal, then you may need higher resolutions.

Viewing Distance Chart
Print Size	Diagonal	
Viewing Distance
(1.5 x Diagonal)
4 x 6"	7.21"	11"	313
8 x 10"	12.81"	19"	181
8 x 12"	14.42"	22"	156
 11 x 14"	17.80"	27"	156
16 x 20"	25.61"	38" (3.17')	89
16 x 24"	28.84"	43"	80
20 x 30"	36.06"	54" (4.5')	64
40 x 60"	72.11"	108" (9')	32
Determining the PPI Needed
The ppi needed for a print with acceptable quality is determined by dividing 3438 by the viewing distance.

3438 ÷ Viewing Distance

3438 is derived from the following formulas.

1 ÷ ppi = 2 x Viewing Distance x tan(.000290888 ÷ 2)

1 ÷ ppi = Viewing Distance x tan(.000290888)

ppi = 3438 ÷ Viewing Distance

.000290888 is the visual acuity angle, a measure of how much resolution the human visual system can perceive.

The above explanation is based on Resolution by Andrew Gregory.

Printing & PPI
The chart below compares the ppi needed for a print with acceptable quality, with the actual ppi.

As you can see, you can use a camera with few megapixels to make quality prints, when viewing distance is also considered.

The figures for PPI Needed, below, are based on the viewing distances in the above chart.

Printing & PPI Flow Chart
2	1600 x 1200	Highest	4" x 6"	313	267	Fair
8" x 12"	156	133	Fair
16" x 24"	80	67	Fair
3	2048 x 1536	Highest	4" x 6"	313	341	Excellent
8" x 12"	156	171	Excellent
16" x 24"	80	85	Good
4	2272 x 1704	Highest	4" x 6"	313	379	Excellent
8" x 12"	156	189	Excellent
16" x 24"	80	95	Good
5	2592 x 1944	Highest	4" x 6"	313	432	Excellent
8" x 12"	156	216	Excellent
16" x 24"	80	108	Excellent
6	3008 x 2000	Highest	4" x 6"	313	501	Excellent
8" x 12"	156	251	Excellent
16" x 24"	80	125	Excellent
7	3072 x 2304	Highest	4" x 6"	313	512	Excellent
8" x 12"	156	256	Excellent
16" x 24"	80	128	Excellent
8	3264 x 2448	Highest	4" x 6"	313	544	Excellent
8" x 12"	156	272	Excellent
16" x 24"	80	136	Excellent
10	3888 x 2592	Highest	4" x 6"	313	648	Excellent
8" x 12"	156	324	Excellent
16" x 24"	80	162	Excellent
Print size, in tandem with viewing distance, are the main determinants of the best resolution needed for a print.

You may want to use the Pixels, PPI, & Print Size Calculators.

Also, consider the following factors.

Next © 2000 - 2018 Jim Beecher

Andrew Gregory's Web Pages
OperaView of Perth city from Kings Park, 31°57'19"S 115°51'2"E
Site Map Help
Home Digicam Resolution

Print Resolution
Visual Acuity and Quality of Light
Distance to Subject
Pixels Per Inch
Dots Per Inch
Camera Resolution
Page Summary
Calculations Form
Links to Other Web Pages

I have been aware of the general consensus of needing between 250 and 300 pixels-per-inch when printing photos to get a good quality print. What I'd never bothered figuring out was why?

This page describes my investigations and turns them into a few simple formulas that help indicate what resolutions, in relation to printing and capture (camera), are needed in various circumstances. I've been pleasantly surprised by how close the formulas match the general newsgroup recommendations.

I hope this information is found to be useful.

The Page Summary at the end of this page includes a form that automates all the calculations shown on this page.

Print Resolution

How much resolution is enough? This is a common question in newsgroups. The answer is simple. It depends!

It depends on several things:

Your visual acuity (the quality of your eyesight)
The quality of light under which you view the subject (photo)
The distance at which you view the subject (photo)
Visual Acuity and Quality of Light

According to the 15th Edition of the Encyclopædia Britannica (1977):

The power of distinguishing detail is essentially the power to resolve two stimuli separated in space, so that, if a grating of black lines on a white background is moved farther and farther away from an observer, a point is reached when he will be unable to distinguish this stimulus pattern from a uniformly gray sheet of paper. The angle subtended at the eye by the spacing between the lines at the point where they are just resolvable is called the resolving power of the eye; the reciprocal of the angle, in minutes of arc, is called the visual acuity. Thus, a visual acuity of unity indicates a power of resolving detail subtending one minute of arc at the eye; a visual acuity of two indicates a resolution of one-half minute, or 30 seconds of arc. The visual acuity depends strongly on the illumination of the test target, ... thus, with a brightly illuminated target, with the surroundings equally brightly illuminated (the ideal condition), the visual acuity may be as high as two. When the illumination is reduced, the acuity falls so that, under ordinary conditions of daylight viewing, visual acuity is not much better than unity.

- Macropædia, Volume 7, page 104.

The article goes on to relate the 30 seconds of arc to the diameter of the light-sensing cones and rods on the retina, establishing 30 seconds of arc (a visual acuity of 2) to be the absolute maximum resolution possible in the human visual system.

Distance to Subject

Clearly, as you view subjects from greater and greater distances, the level of detail you can see diminishes. The distance between the details is best measured by the angle between them as you view them. As they move further away, the angle diminishes, and thus the detail also diminishes.

The minimum angle between the details was established above, under Visual Acuity, as 30 seconds of arc under ideal conditions and one minute of arc under ordinary conditions.

The relationship between angle, distance and detail separation is given by the formula (see Math Forum: Ask Dr. Math FAQ: Circle Formulas):

c = 2 × d × tan( θ ÷ 2 )

where c (the chord length) is the detail separation distance, d (the distance to the chord midpoint) is the viewing distance, and θ (the angle in radians) is the visual acuity angle.

To aid the maths, the angles given above in degrees have been converted to radians (see Dr. Math item):

Visual Acuity Angles in Radians
Angle	... in Radians
30 seconds of arc	0.000145444
1 minute of arc	0.000290888
Pixels Per Inch

To show how this works in practice, consider a standard 6 by 4 inch print. It depends on the person, but these might typically be viewed at a distance of 15 inches.

Basing the calculation on ordinary (typical) viewing conditions where the visual acuity angle is 0.000290888 radians (θ), the distance (D) between two details such that they are just distinguishable when viewed from a distance of 15 inches (V) is:

D = 2 × V × tan( θ ÷ 2 )
D = 2 × 15 × tan( 0.000290888 ÷ 2)
D = 0.004363323

The reciprocal of that is the "details per inch" = 229. This would be the minimum "pixels per inch" required for printed details to be at the limit of visual resolution under ordinary conditions.

A larger print, intended to be viewed at a distance of, say 30 inches, would require a minimum PPI of 115.

A quick way to determine the minimum PPI resolution to print your photos is to divide 3438 by the intended viewing distance in inches. This is for ordinary conditions; double the number for ideal conditions.

Where did "3438" come from? Given the visual acuity angle for ordinary viewing, the equation can be written as:

1 ÷ PPI = 2 × V × tan( 0.000290888 ÷ 2)
1 ÷ PPI = V × 0.000290888
PPI = 3437.746747 ÷ V

Dots Per Inch

Pixels in your photo image are not the same as dots printed on your photo paper. Each pixel on your screen can be one of 16 million different colours. Printers have a much more limited range of colours per dot. At minimum it is the number of different colour ink tanks installed in the printer, plus one (for white - the blank paper). Some printers are capable of overprinting their colours, giving their printed dots a wider range of colours.

For example, my HP Officejet G95 uses the HP PhotoRet III "colour layering technology". The printer has four inks - black, cyan, magenta, and yellow. According to HP technical documentation, the PhotoRet III technology can produce over 3500 different colours per dot. Different printers with more ink tanks (the additional colours usually being light cyan, light magenta, and light black) will be able to produce more colours per dot.

In any case, no matter the technology or the number of ink colours, printers simply cannot come anywhere near the 16 million different colours per pixel your images are capable of.

Printers address this problem by printing smaller dots and more of them. The same principle that causes a fine weave of black and white threads to appear gray from a distance is used to make the small number of colours available to a printer appear to be a much wider range of colours when viewed from a distance, even if that distance is only a few inches.

There is no simple method to determine the DPI to print a photo at. Clearly, it's related to the viewing distance and, by extension, the PPI. The DPI value must exceed the PPI value by a significant amount in order for the colours of the printed dots to blend imperceptibly.

The amount by which the DPI must exceed the PPI depends on how the printer makes up the extra colours. The fewer colours the printer is able to produce per dot, the more dots are required to spread the average colour around.

The short answer is, print at the highest DPI your printer allows. For printers that allow a trade-off between resolution and colours-per-dot (like my OfficeJet), the only way to determine which is best is to try the different configurations and see for yourself which is better. I can't tell the difference in quality, but the "lower-resolution-with-more-colours-per-dot" configuration prints faster for me.

Camera Resolution

If the assumption was made that digital cameras can record the full 16 million different colours per pixel, the calculation to determine the required resolution would be simple. Take your required print size in inches and the PPI you calculated for the required viewing distance and multiply them togther.

For example, a 6 by 4 inch print to be viewed at 15 inches would require a minimum (6 × 229) × (4 × 229) = 1374 × 916 = 1258584 pixels = 1.2 megapixels.

However, digital cameras are not capable of capturing 16 million different colours per pixel. Instead they use a colour filter (called a Bayer filter) made up of red, green, and blue and measure 256 different shades of each. My Inside my QV-3000 web page has close-up photos of a CCD where you can see the filter. How Stuff Works has a page describing the process.

(Note that recent innovations, in particular the Foveon X3, are expected to remove this limitation and result in cameras capable of measuring the full 16 million colours at each pixel.)

The process to convert these separate colours reduces the effective resolution of the camera by at least half. Therefore, the required megapixels calculated above should be doubled to 2.4 megapixels.

Rearranging the maths will result in a simpler formula. All dimensions in inches or square inches as appropriate.

Megapixels (MP) = (Bayer filter correction) × (print width × PPI × print height × PPI) ÷ 1000000
MP = 2 × (print area × PPI²) ÷ 1000000
PPI = (3437.746747 ÷ viewing distance (V) )
PPI² = (11818102.69 ÷ V²)
MP = 2 × (print area × 11818102.69 ÷ V²) ÷ 1000000
MP = (print area × 23.63620539 ÷ V²)

Using the previous example, the 6 by 4 inch print has an area of 24in². The square of the viewing distance is 225. The required megapixels are (24 × 23.6) ÷ 225 = 2.5.

Page Summary

What these formulas are calculating is the resolution beyond which any higher resolution is pointless. Your personal preferences may allow the resolution to be lower. Note also that where your printers DPI does not greatly exceed the PPI of your prints, the quality will be poorer and will need to be viewed at distances greater than those indicated here.

These numbers are for high quality under 'ordinary' conditions. Double the PPI and quadruple the MP for 'ideal' conditions.

For highest quality prints, scale your photos so that the PPI is no smaller than the value indicated by the formula:

PPI = 3438 ÷ (viewing distance in inches)

Print your photos at the highest dots-per-inch (DPI) your printer allows. Preferably, the printer DPI should triple (or more) the image PPI.

When performing the rescaling in your photo editor, do not select the resample option. You will either have more pixels than is strictly required, in which case the printer driver will happily 'down-sample' your photo automatically. The extra pixels may even help it produce a slightly better print. If you don't have enough pixels than the maths would indicate, then there isn't anything you can do about it. Pixels cannot be invented and you'll have to make the best of those you have.

For example, if you're printing a photo intended for viewing at a distance of 15 inches, the minimum PPI to aim for is 3438 ÷ 15 = 229, and your printer DPI should exceed 687.

To determine the required megapixel resolution of the digital camera, use this formula:

MP = (print area in square inches) × 23.6 ÷ (viewing distance in inches)²

For example, a 6 by 4 inch print to be viewed at 15 inches will require a minimum (6 × 4 × 23.6) ÷ 15² = 566.4 ÷ 225 = 2.5 megapixels.

Calculations Form

NOTE: Units are not specified since they do not affect the numbers. The numbers you enter must all use the same units, of course! If the width and height are inches, then the viewing distance must also be entered in inches (and vice versa), and the calculated PPU will be pixels per inch.

Resolution Calculation
Visual Acuity (explanation) (0.04 - 2):
(1 = ordinary, 2 = ideal)	
Bayer filter correction factor (explanation):
(eg, 2:Bayer filter halves camera resolution)	
Print width:	
Print height:	
Viewing distance (explanation):
(6 year old child - minimum 2.5 inches,
30 year old adult - minimum 6 inches,
table top to eye - ~20 inches)	
PPU Constant:
PPU = this ÷ viewing distance	
MP Constant:
MP = print area × this ÷ (viewing distance)²	
PPU - Maximum pixels/unit:	
MP - Maximum Megapixels:	
Links to Other Web Pages

For a bit of a background on resolution, see Scanning Basics 101 - All about digital images by Wayne Fulton.

The Luminous Landscape has several tutorials on Resolution and Sharpness that may be of interest.

Terry Dawson has some relevant pages too.

Last updated: 2004-06-19. Copyright © 1999-2019. 
Opera, the fastest and most secure web browser
Top of Page Site Map Help
HomeContact Me