Why Projector Lumens Are a Screen Area

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The honest answer starts with the fact that the two products are not sold in comparable units, and nobody mentions it. A television is specified in nits, which is a brightness. A projector is specified in lumens, which is a total quantity of light with no area attached. You cannot compare them until you decide how big the picture is, and the screen is usually bought separately, later, by diagonal.

So here is the conversion, done once. Two hundred lumens on a 100 inch screen is 25.4 nits. A portable monitor in our own catalogue publishes 270. That is a factor of 10.6, and it is not a scandal, because the number a cinema is built around is 48.

One line of arithmetic, and it is the whole of it

For a screen that scatters light diffusely, the luminance is the illuminance falling on it multiplied by its gain and divided by pi. The illuminance is just the flux divided by the area. That is the entire conversion.

Start with the area, because the diagonal is not it. A 100 inch 16:9 screen has a diagonal of 100 inches, so its width is 100 times 16 divided by the square root of 337, which is 87.16 inches, and its height is 49.03 inches. In metres that is 2.2138 by 1.2453, so 2.75671 square metres.

An HP MC425 smart projector publishes 200 ISO lumens, native 1080p with 4K signal support, Android TV built in, AI auto focus and keystone, WiFi 6, Bluetooth 5.4, a short-throw 0.8:1 lens and the ability to run from a 65 watt USB-C power bank.

Two hundred lumens over 2.75671 square metres is 72.55 lux. Our roundup of projector screens for a cinematic movie-night setup publishes the other input: a gain of 1.1 for the MaxWhite 2 material on its 100 inch pick, with a 180 degree viewing angle. So the luminance is 72.55 times 1.1 divided by pi, which is 25.40 candelas per square metre.

On the 120 inch screen from the same page the area is 3.96966 square metres and the answer is 17.64 nits.

What 25.4 nits is actually like

Three comparators, and two of them come off our own pages.

Our roundup of portable touchscreen monitors for mobile work publishes a panel at 270 nits and is blunt about where that leaves it: "at 270 nits it trails the brightest panels here, so glare in strong light is a limit". The projector on 100 inches is a tenth of that trailing panel. Another of our pages publishes a 500 nit screen, which is 19.7 times.

And then the number that reframes it. The reference luminance for two-dimensional cinema projection is 48 candelas per square metre. The projector on a 100 inch screen reaches 52.9 percent of that, and on 120 inches 36.8 percent.

So 200 ISO lumens is not a scandal and it is not a home cinema either. It is about half of what a commercial cinema puts on its screen, and a commercial cinema is a room with no windows, black walls and the lights off. The record for the projector arrives at exactly the right advice without the arithmetic: "it looks great in a properly dark room but washes out in a bright or daylight-lit room. That is true of most portable projectors, and it is the single biggest thing to get right: use it after dark or with the room blacked out."

Our own guide to choosing a projector opens with the same instruction, and it is the right one: "Start with your room, not the projector." The next two sections are what that sentence is worth in numbers.

Every ten percent of diagonal removes seventeen percent of the brightness

Area goes as the square of the diagonal, so luminance goes as one over the square of the diagonal. This is the single most useful consequence of the conversion and it is never stated in the units people shop in.

From 100 to 120 inches is a factor of 1.2 in diagonal and 1.44 in area, so 30.56 percent of the brightness is gone and 25.40 nits becomes 17.64. From 100 to 150 inches is 2.25 times the area, so 55.56 percent is gone and you are at 11.29 nits, which is 23.5 percent of the cinema reference.

In general, every 10 percent added to the diagonal removes 17.36 percent of the luminance. That is the exchange rate between picture size and picture brightness, it holds for any projector and any screen, and it is the number to carry into a screen decision.

One honest softening, because the arithmetic is harsher than the experience. Our page on what a 100,000 hour LED rating actually promises sets out the relevant point: "perceived brightness does not track luminance linearly. It follows roughly a power law." At the conventional exponent of about a third, a 30.56 percent drop in luminance reads as about an 11.3 percent dimming to the eye. So going from 100 to 120 inches is a real loss and it is a tenth rather than a third. What it is not is free.

The room is a competing projector

Here is the result that makes the whole category make sense, and it follows from the same formula applied twice.

A screen does not only reflect the projector. It reflects the room. Whatever ambient illuminance falls on the screen comes back at the same gain over pi, and that reflection sets the floor of the image. The darkest thing on the screen can never be darker than the room bouncing off it.

Take a dim living room at 100 lux. The screen's own black level is 100 times 1.1 divided by pi, which is 35.01 nits. The projector's full white is 25.40. The room is brighter than the picture, and the on-screen contrast ratio is 60.41 over 35.01, which is 1.73 to 1.

Turn the lights down to 10 lux. The black level becomes 3.50 nits and the contrast becomes 8.26 to 1.

Black the room out to 1 lux. The black level becomes 0.35 nits and the contrast becomes 73.6 to 1.

That is a factor of 42.6 in contrast ratio, achieved by touching the curtains and not the projector. No projector upgrade available at any specification does that, because adding lumens raises the white and leaves the black exactly where the room put it. This is why "start with your room" is not a preamble. It is the main lever, and it is 42.6 times stronger than anything on the box.

The figures above leave out the projector's own black floor, which only makes them flattering. Add it and every contrast number falls.

A pen light with four times the flux

If a lumen figure still feels like a brightness, this is the check that cures it. A HOKOILN 800 lumen rechargeable dual-beam pen light publishes 800 lumens from its spotlight, a reach of up to 100 metres, up to 4 hours of runtime, a side COB floodlight good for 50 metres, an anodized aluminium body rated for a 1.5 metre drop and a 5.78 inch body weighing 1.51 ounces.

Eight hundred lumens is four times the projector's 200. Spread that flux over the same 100 inch screen and you would get 101.6 nits, four times the picture. A thing that clips to a hat brim contains four times the luminous flux of a device sold to fill a wall.

The difference, of course, is where the light goes. The pen light concentrates its flux into a narrow cone, which is why it reaches 100 metres, and our page on whether more lumens mean a light shines further works that chain out properly through candelas and lux. This page is the other branch of the same fork: flux divided by area, for a surface that scatters. Same unit, two completely different questions, and a projector is the second one.

The pen light is also the most honest listing in this group and it should be said plainly: "all lumen, distance, and runtime numbers are maker-stated rather than lab-verified", repeated again in its drawbacks. That caveat applies to every photometric figure on this page and only one product states it.

The throw distance that takes one multiplication

The projector publishes a 0.8:1 throw ratio, which is a short throw, and our screens page correctly tells you to check the geometry: "Use the projector's throw calculator or official manual to find the lens-to-screen distance for the selected image size."

For this projector that calculator is a multiplication. A throw ratio is the lens-to-screen distance divided by the image width, so for a 100 inch screen 0.8 times 2.2138 metres puts the lens 1.771 metres from the wall, which is 69.7 inches. For the 120 inch screen it is 2.125 metres, or 83.7 inches. Those are the two numbers a reader actually wants and they are one line apiece.

Which uncovers a problem that neither page can see on its own. Our screens page says of the 100 inch pick that "Elite Screens marks the Manual B material as incompatible with those projector types", meaning short-throw and ultra-short-throw, and repeats it: "The M100H is specifically excluded from short-throw and ultra-short-throw use."

The only projector we carry has a short-throw lens. The only 100 inch screen we recommend is marked incompatible with short-throw projectors. Both statements are correct and the two pages do not compose, which is worth knowing before anyone buys the pair. The 120 inch freestanding screen on the same page carries no such exclusion, and at 17.64 nits it is the dimmer of the two options.

A gain above one is borrowed, not free

While that screen page is open, there is a second figure on it worth reading carefully. It publishes a 1.1 gain and a 180 degree viewing angle for the same material.

Screen gain is measured against a perfect Lambertian reflector of unit reflectance, so a gain above 1 cannot come from reflectance. No white diffuser gets above about 0.90, and a Lambertian screen at 0.90 reflectance has a gain of 0.90. To publish 1.1 you have to narrow the distribution and concentrate light on axis, and against a realistic 0.90 that is about 22 percent of concentration taken from the edges of the room and given to the middle.

The two figures are not contradictory. A 180 degree figure is normally the total angle over which the image remains visible, not the angle over which brightness holds. But 1.1 is easy to read as 10 percent of free brightness, and it is not free: it is 22 percent of redistribution, and the seats it comes from are the ones at the sides.

On the arithmetic of this page, a gain of 1.1 against a plain 0.90 wall takes 25.40 nits to 20.78 and back again, which is 22 percent, which is bigger than the difference between a 100 and a 110 inch screen. Gain is the easiest nit on the list to obtain and it is bought with viewing angle.

Two coverage figures with no light attached

A Govee star projector with a 7-zone nebula effect publishes seven individually controllable zones, a stated 540 square feet of coverage from wide field of view lenses, Matter compatibility, more than 50 scene modes, 18 white noise options, a sleep timer, a 6.18 by 5.51 by 8.94 inch body and a twelve month warranty. It publishes no luminous flux of any kind.

Five hundred and forty square feet is 50.17 square metres, which is eighteen times the 100 inch screen above. Without a flux figure there is no way to know whether the pattern is visible at the far corner of that area, because the same conversion applies: luminance is flux over area, and one of the two terms is missing.

Its own record is right about why the coverage is wide, and the sentence is unusually clear about what the number is not: the figure "comes from the lens design rather than brute brightness, which is the right approach. Wide field of view lenses spread the pattern further without needing more output". That is correct, and it is also the admission. A wider lens over the same output means a larger area and a proportionally dimmer pattern, which is the projector arithmetic above running on a ceiling instead of a wall.

This is the same gap, in the same shape, as the one on our page about why a grow light's coverage area needs a height, where a published footprint turned out to depend entirely on an unpublished beam angle. A coverage area is half a specification. The other half is a flux.

A Stecutts artificial blue skylight is the clearest case of the gap, because its entire proposition is photometric. It is sold as a 2 by 2 foot ceiling panel that "reproduces the light of the sun and the sky", with a sunrise to sunset rhythm, brightness from 1 to 100 percent, colour temperature from 2000K to 8000K, light refracting at 40 degrees onto the wall, and a requirement for a 2 by 2 foot ceiling opening at least 9.5 inches deep.

Every one of those is a real specification and not one of them is a lumen, a lux or a nit. Take a representative 4,000 lumens for a 2 by 2 foot LED panel of that kind, which is 0.3716 square metres. In a 12 by 12 foot room, which is 13.378 square metres, that is 299 lux at the floor. Outdoor illuminance on a bright overcast day is around 10,000 lux and full sun is around 100,000, so the panel is delivering something like 3 percent of an overcast day and 0.3 percent of sunshine.

That is not a criticism of the product, which is clearly doing something people want in basements. It is a statement about which claim is being made. The panel reproduces the appearance of a sky, convincingly by all accounts, and it does not reproduce its illuminance, and the figure that would make the distinction is the one figure the listing does not carry. Its drawbacks are careful about everything else, including "Do not look directly at the light on strong mode", which is a luminance warning on a product with no published luminance.

The honest limit, and the answer to the question

What is exact here is the conversion and everything that follows from it. Luminance is illuminance times gain divided by pi. Illuminance is flux over area. The area of a 16:9 screen follows from its diagonal. So the 25.40 nits, the 17.64, the 30.56 percent, the 17.36 percent per ten percent of diagonal, and the three contrast ratios are arithmetic on published figures with nothing modelled in between. The 101.6 nits from a pen light's published 800 lumens is the same calculation run on a different flux.

What is representative is the room. The 100, 10 and 1 lux ambient levels are ordinary figures for a lit living room, a dark one and a blacked-out one, and they are not measurements of anyone's house. If your room is 30 lux the contrast is 3.4 to 1 rather than 1.73 or 8.26, and the lesson is unchanged. The 48 candelas per square metre cinema reference is a standards figure, the 0.90 screen reflectance is a typical value for white diffusing material, the cube root exponent for perceived brightness comes from our own LED page rather than from this one, and the 4,000 lumens for the skylight panel is an assumption standing in for an absent specification.

What this page deliberately does not do is compute a contrast ratio for the projector itself. That needs a black level in the same units as the white, and our own guide is right that the figure "is quoted inconsistently, so treat it with caution", which is exactly why nothing here depends on it. The ambient arithmetic above deliberately uses a projector black of zero, which flatters every result, and the real numbers are worse by an amount no listing publishes. Nor has it compared image quality in any sense beyond brightness, because resolution, colour and motion are not things a lumen figure can answer and the honest reading of a native 1080p panel is the one our own guide already gives.

And the answer to the question, which was projector or television. On brightness alone it is not close: the published figures put a 200 lumen portable at a tenth of a mid-range portable monitor and about half of a cinema screen, and the television wins in any room with a window open. What the projector buys is size, and the exchange rate is the one firm number on this page, 17.36 percent of brightness for every 10 percent of diagonal. So the decision is really about whether you can supply the room, because a blacked-out room is worth a factor of 42.6 in contrast and no amount of specification is worth anything close. If you can make the room dark, a modest projector on a modest screen is a genuinely cinematic 53 percent of cinema. If you cannot, the arithmetic says buy the panel, and our guide to reading projector specifications says the same thing in words.