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A Simple Guide to Calculating Lumens

How bright a projector you need to light up a screen—whether in a dark room with controlled lighting or in a family room or conference room with window light that changes throughout the day—is easy to determine, in principle at least. Start with the screen size and the image brightness you need, and then calculate how many lumens it will take to give you that desired image brightness.

Unfortunately, it's not so simple in practice, with all sorts of ifs, ands, and buts to account for. Then there's the math part of it to negotiate. There's not much you can do about most of these complications, but in this article I'll address one in particular. When it comes to calculating the lumens you need, you can replace most of the arithmetic with a simple look-up table, which you'll find at the end of this article.

MathProblem main slider2 100
Calculating your lumen needs for a particular screen size and lighting doesn't have to be so hard...

If you already know the screen size and image brightness you want, you can skip to the section on calculating lumens. If not, you'll probably find it helpful to at least touch on those two steps first.

Screen Size and Seating Distance

Deciding on screen size is worth an article of its own. Indeed, ProjectorCentral's Paul Vail discussed the issue in a Q&A column answering the question, "How Do I Calculate Screen Size and Seating Distance for My Home Theater?". Beyond that, if you search the Web, you'll turn up several competing rules of thumb for the ideal seating distance for any given screen size.

Among the most common suggestions are to multiply the diagonal measurement of the screen by 1.6, 1.5, or 1.2 times to get the best seating distance, or divide the diagonal measurement by 0.6 or 0.84. Either approach—multiplication or division—will give you left and right viewing angles for the image of roughly 30 to 40 degrees, which is the usual recommended range. Other sites give rules of thumb in terms of the height or the width of the screen, telling you to sit no closer than two times the width and no farther than five times the width, for example, though five times is a little far for my taste.

The ranges these formulas give you are most useful for choosing a screen size in a room with multiple rows for seating, since they'll tell you where the front and back rows should be. But if you're trying to find the right screen size to watch from a couch in your family room, personal preference matters more. If you like sitting towards the back of the theater when you go to the movies, pick a seating-distance-to-screen-size ratio in the recommended range that gives you a smaller screen. Prefer the front row? Pick the ratio that gives the bigger screen. Insist on being in the middle row? Use a ratio in the middle of the range.

Also keep in mind that if you're trying to find the right size screen for a room that already has a couch or other seating in place, so you already know the distance, you'll want to flip the equation around to solve for screen size. If you start with the rule that Distance = ScreenDiagonal / 0.84, for example, the ScreenDiagonal = Distance X 0.84.

Image Brightness

You can also find competing rules of thumb for best image brightness for different lighting conditions. But as with screen size, the best brightness is also partly a matter of personal taste. For a dark room, for example, the most common brightness recommendation is 16 foot-lamberts (ft-L), though I've seen suggestions as high as 30 to 40 ft-L. That 16 ft-L recommendation is derived from the Society of Motion Picture and Television Engineers (SMPTE), which defines a target of 16 ft-L but actually allows a range of 12 ft-L to 22 ft-L. I've found that when I set up a projector for testing in a dark room by subjectively judging it for a balance of good contrast and comfortable brightness for viewing, I typically wind up at the high end of that range.

Recommendations for ambient light viewing have even greater variation. That's partly because your family room may be brighter than mine, and partly because there's a big difference between the image being bright enough to give you vibrant color and good contrast and it being merely bright enough so the image isn't hopelessly washed out. Here again, personal preference rules. However, a common recommendation for a family room is 50 ft-L, with a warning that you may need to adjust it somewhat, since home lighting levels vary.

The key point here is that you should take whatever guidelines you're working from for the ideal screen size, seating distance, and image brightness as rough rules of thumb, not iron-clad truths that you have to match exactly. If you've had some experience with projectors, you should already have a sense of your personal preferences and how closely they match what the formulas tell you. If you're moving up from a large screen TV, try applying the seating distance formula to watching a movie on the TV, and see whether you like the result, or would rather modify it. [Editor's note: Here are two more tricks used by installers to help clients settle their preferred screen size after the calculations have been made: (1) borrow a projector—any projector—and blast up your expected image size on the screen wall to get a sense of how it'll look from your seating distance; or (2) tape out the screen dimensions on the screen wall with blue painter's tape, then step back and have a look. Be gentle with the tape, though, to avoid pulling off any old paint.—R.S.]

In any case, once you know the screen size and brightness you're aiming for, your next step is to find the lumen level for your projector. Personal preference has nothing to do with that. It's the one step in this process that's simply about the calculation.

Calculations with Less Arithmetic

So, how many lumens do you need? The formula for the calculation is straightforward:

Lumens = ft-L X SquareFeet / Gain

where SquareFeet is the screen area in square feet and Gain is the screen's gain.

As simple as the formula is, finding the square footage is a little cumbersome. If you start with the diagonal screen size you want, you have to first determine the height and width, multiply the two numbers to get the square inches, and then convert to square feet. Similarly, if you start by deciding the height or width, you have to do pretty much the same thing.

That's a lot of arithmetic, particularly if you're setting up a room from scratch and considering more than one screen size. To make the process easier (not to mention faster), you can use the tables at the end of this article to look up the square footage of any 16:9 or 16:10 aspect ratio screen size from 75-inch to 150-inch diagonal by it's diagonal size, width, or height. The range was chosen to cover any size you're likely to be considering for a home theater and for most conference rooms. The tables can also serve double duty if you're still deciding on a screen size and need to see what diagonal size will fit in the available height or width in your room.

Incidentally, you may be familiar with an alternate formula for converting ft-L to lumens, namely:

Lumens = ft-L X Diagonal X Diagonal/(337 X Gain)

where Diagonal is the diagonal screen size and Gain is the screen's gain. The two formulas both give the same answers for screens with 16:9 aspect ratios, but the second works for 16:9 format only. (Fun fact: 337 equals 162 plus 92.) The first formula works for any aspect ratio, and I'd argue there's less arithmetic to do. There's certainly less if you use the tables in this article. Here's how to use them:

Assume you're setting up a home theater in a room with controlled lighting, have decided on a 110-inch screen—which is a popular size—and have also decided to stay with the SMPTE guidelines and target a 16 ft-L brightness. Since it's for a home theater, you'll want to choose the table for a 16:9 aspect ratio rather than the one for 16:10. An abbreviated version of the table looks like this:

Sample Table for 16:9 Aspect Ratio

Diagonal (inches) Width (inches) Height (inches) Area (Square Feet)
108 94 53 34.6
109 95 53 35.3
110 96 54 35.9
111 97 54 36.6
112 98 55 37.2

Simply browse through the column showing diagonal size till you get to the line showing a 110-inch diagonal, and look across the line to find the area in square feet. Note also that if you picked a size using one of the rules that starts with height or width, the table lets you find the right area in square feet using either of those two parameters instead

The arithmetic now reduces to plugging the number from the table into the formula along with the 16 ft-L you've already decided on, which in this example gives you:

Lumens = 16 ft-L X 35.9 Sq Ft / Gain

Don't worry about gain just yet; treat it as 1.0. Doing the math gives you 574 Lumens, which you can likely get using the ECO mode in most projectors. And if the lowest brightness the projector offers is a bit higher, it may well still be in the 12 to 22 ft-L range. If you have the actual lumen measurements for your projector, you can calculate the ft-L, using the formula:

ft-L = Lumens X Gain / SquareFeet

Needless to say, this, and all the other math in this example, will be even easier if you set up the equation in a spreadsheet so you can just enter any variations on any number into a cell and instantly see the answers.

Now lets assume that instead of watching only in a dark room, the projector's going in your family room, where you might turn out the lights occasionally, but will generally be watching with some lights on and need 60 ft-L—the number that works in my family room.

Do the math for the 60 Ft-L image brightness, and you get:

60 ft-L X 35.9 Sq. Ft = 2154 lumens

It's easy to find projectors with this brightness level in their best color mode, but in many cases you'll have to use the full power mode, and you may find the projector dipping below the brightness level you need as the lamp ages and loses brightness. You can address this possibility by considering brighter projectors, smaller screen sizes, or by literally adding gain into the equation. Factoring in a screen with a 1.1 gain brings the lumen requirement down to 1,958 lumens. At 1.2 gain, it drops to 1,795. And at 1.3 gain, it drops to 1,656.

When You Need to Rethink Screen Size

The table can also be useful if you decide you need to rethink the screen size. If you plan to watch in the daytime very often, for example, you'll need a much higher image brightness. In my family room, for example, even on an overcast day, the minimum brightness for watching a brightly lit scene like a newscast or sports without colors looking dull and contrast being washed out is 60 ft-L. For movies or TV shows with darker scenes, colors and contrast are wanting at anything less than 95 ft-L.

For a 110-inch screen, that translates to roughly 2,625 lumens even with a 1.3 gain screen (95 X 35.9 / 1.3), and the needed brightness is even higher on bright, sunny days. Rather than up your budget for a brighter, more expensive projector, you might want to turn the equation around so you can calculate the area in square feet that you can light up with the lumen brightness you can afford, and then look through the table, to find what size screen that translates to. The formula for finding the area in square feet is:

SquareFeet = Lumens X Gain / ft-L

About 16:10 Projectors and 2.4:1 Content and Screens

If you're setting up a conference room with a native 16:10 business projector and matching screen, all the same considerations apply, except for the actual numbers you'll find in the 16:10 table.

When setting up a native 16:10 projector as a home theater projector to watch 16:9 content, however, there's an additional twist to keep in mind. In most cases you'll be using only 90% of the area on the projector's imaging chip or chips, which means you'll be using only 90% of its brightness in lumens. Be sure to correct for that 10% difference in your calculations.

If you use the full lumen measurement for the projector as your starting point, compare it to 1.1 times the lumen requirement the formulas give you. Alternatively, if you start with the lumen brightness that the formulas give you, compare it to 0.9 times the projector brightness at 16:10.

In addition, note that everything discussed here also applies to using a 16:9 or 16:10 projector with letterbox bars above and below the 2.4:1 content. However, there are additional considerations if you're using a constant image height setup with a 2.4:1 screen. The specifics vary depending on the projector's native aspect ratio and whether you're using an anamorphic lens or not, all of which adds up to enough variations to make them best dealt with in a separate article. In the meantime, the information above and the tables below should make the task a lot easier when trying to determine the right lumen brightness for 16:9 or 16:10 installations.

TABLE: Projection Screen Dimensions & Area, 16:9 Aspect Ratio

Diagonal (inches) Width (inches) Height (inches) Area (Square Feet)
75 65 37 16.7
76 66 37 17.1
77 67 38 17.6
78 68 38 18.1
79 69 39 18.5
80 70 39 19.0
81 71 40 19.5
82 71 40 20.0
83 72 41 20.4
84 73 41 20.9
85 74 42 21.4
86 75 42 21.9
87 76 43 22.5
88 77 43 23.0
89 78 44 23.5
90 78 44 24.0
91 79 45 24.6
92 80 45 25.1
93 81 46 25.7
94 82 46 26.2
95 83 47 26.8
96 84 47 27.3
97 85 48 27.9
98 85 48 28.5
99 86 49 29.1
100 87 49 29.7
101 88 50 30.3
102 89 50 30.9
103 90 50 31.5
104 91 51 32.1
105 92 51 32.7
106 92 52 33.3
107 93 52 34.0
108 94 53 34.6
109 95 53 35.3
110 96 54 35.9
111 97 54 36.6
112 98 55 37.2
113 98 55 37.9
114 99 56 38.6
115 100 56 39.2
116 101 57 39.9
117 102 57 40.6
118 103 58 41.3
119 104 58 42.0
120 105 59 42.7
121 105 59 43.4
122 106 60 44.2
123 107 60 44.9
124 108 61 45.6
125 109 61 46.4
126 110 62 47.1
127 111 62 47.9
128 112 63 48.6
129 112 63 49.4
130 113 64 50.1
131 114 64 50.9
132 115 65 51.7
133 116 65 52.5
134 117 66 53.3
135 118 66 54.1
136 119 67 54.9
137 119 67 55.7
138 120 68 56.5
139 121 68 57.3
140 122 69 58.2
141 123 69 59.0
142 124 70 59.8
143 125 70 60.7
144 126 71 61.5
145 126 71 62.4
146 127 72 63.3
147 128 72 64.1
148 129 73 65.0
149 130 73 65.9
150 131 74 66.8

TABLE: Projection Screen Dimensions & Area, 16:10 Aspect Ratio

Diagonal (inches) Width
(nearest inch)
Height
(nearest inch)
Area (Square Feet)
75 64 40 17.6
76 64 40 18.0
77 65 41 18.5
78 66 41 19.0
79 67 42 19.5
80 68 42 20.0
81 69 43 20.5
82 70 43 21.0
83 70 44 21.5
84 71 45 22.0
85 72 45 22.5
86 73 46 23.1
87 74 46 23.6
88 75 47 24.2
89 75 47 24.7
90 76 48 25.3
91 77 48 25.8
92 78 49 26.4
93 79 49 27.0
94 80 50 27.6
95 81 50 28.2
96 81 51 28.8
97 82 51 29.4
98 83 52 30.0
99 84 52 30.6
100 85 53 31.2
101 86 54 31.8
102 86 54 32.5
103 87 55 33.1
104 88 55 33.8
105 89 56 34.4
106 90 56 35.1
107 91 57 35.7
108 92 57 36.4
109 92 58 37.1
110 93 58 37.8
111 94 59 38.5
112 95 59 39.2
113 96 60 39.9
114 97 60 40.6
115 98 61 41.3
116 98 61 42.0
117 99 62 42.7
118 100 63 43.5
119 101 63 44.2
120 102 64 44.9
121 103 64 45.7
122 103 65 46.5
123 104 65 47.2
124 105 66 48.0
125 106 66 48.8
126 107 67 49.6
127 108 67 50.3
128 109 68 51.1
129 109 68 51.9
130 110 69 52.7
131 111 69 53.6
132 112 70 54.4
133 113 70 55.2
134 114 71 56.0
135 114 72 56.9
136 115 72 57.7
137 116 73 58.6
138 117 73 59.4
139 118 74 60.3
140 119 74 61.2
141 120 75 62.1
142 120 75 62.9
143 121 76 63.8
144 122 76 64.7
145 123 77 65.6
146 124 77 66.5
147 125 78 67.4
148 126 78 68.4
149 126 79 69.3
150 127 79 70.2
Comments (4) Post a Comment
Daniel Posted Oct 17, 2019 1:37 PM PST
How about for HDR projection? 16 ft-L may be fine for SDR, but is there a target to hit for HDR?

I suppose, since no home theater projector could hope to achieve the peak nits required for "full HDR", the recommendation would be the brightest projector possible that also provides acceptable black levels. So now we have to balance between peak brightness and deep blacks. Some people prefer the JVCs with their deep blacks and acceptable brightness, whereas others prefer something like an LK990 with it's high peak brightness, and grey blacks.

And then there's that Christie that does both... and costs more than a house.
Rob Sabin, Editor Posted Oct 17, 2019 4:20 PM PST
Daniel, these are good questions and good observations regarding the trade-off between peak whites and good blacks in a home theater environment. Regarding the light output on screen for HDR, there's a lot of opinion on this. I personally set up projectors on my 92-inch home screen to typically hit about 25-30 ft-L peak white with HDR, which usually isn't too hard to do on such a small screen in total darkness (the only way to watch HDR, frankly), and about 16-20 ft-L for peak white on SDR. Some people like even brighter. Although you do bring your blacks up a bit when you raise the peak white, the HDR tone mapping in a specific projector has an even greater effect on the sense of overall contrast and the simultaneous rendering of the highlights and darker parts of the image than where you end up for the peak whites, which you'll likely adjust anyway to taste with any given content using the projector's HDR brightness control.
John Vincent Posted Oct 22, 2019 10:14 AM PST
We are having a debate about 5000 & 6000 lumen projectors for classroom and auditoriums.

I can understand a 6500 lumen projector in a 200 person auditorium but a 6500 lumen projector in a 40 or 60 person classroom seems like its over the top.

But the integrator is pushing for 6500 lumen projectors in all the room yet we run 5000 lumen in classrooms and they seems to be working well.

Can having too much lumen power be a problem?
Rob Sabin, Editor Posted Oct 22, 2019 11:30 AM PST
John, although having too much brightness in a dark room can be fatiguing on the eyes, for brightly lit environments its hard to argue with the wisdom of extra lumens, particularly if these are brightly lit rooms or ones with windows that bring in a lot of natural light. Keep in mind that there are different preset modes in every projector as well, and there's a chance that the brightest output mode that provides that 6,500 lumens could be too green for any real use and that you'll end up with something less than than full power in your classrooms. Also that the integrator, who has already accounted for either the screen size you have now or the possibility you might want a larger one in the future, will have the brightness reserves to tune the projector very specifically to the needs of each environment. It may come down to budget, and I would agree that 5,000 lumens is probably a good size for a moderate classroom projector. But those other factors I mentioned (as well as the required throw distance) all come into making that determination, and if you're upgrading your projectors, stepping up on brightness is usually a good idea. I'd ask the integrator to explain his rationale for the lumen spec he's recommending and see if he has a reasonable explanation aside from wanting to sell you a more expensive projector.

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