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.
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.
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 / Gainwhere 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)|
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)|
TABLE: Projection Screen Dimensions & Area, 16:10 Aspect Ratio
|Area (Square Feet)|