Screen Brightness Calculator
Enter a projector's brightness in lumens, the size of the screen and its gain to estimate the average illuminance on the screen and its luminance in nits (cd/m²) and foot-lamberts (fL).
Lumens, lux and nits are different things
- Luminous flux (lumens, lm) is the total light a projector puts out. This is the number in the catalog.
- Illuminance (lux, lx, or foot-candles, fc) is how much of that light lands on each unit of the screen. 1 lux is 1 lumen on 1 square meter. 1 foot-candle is 1 lumen on 1 square foot.
- Luminance (nits, cd/m², or foot-lamberts, fL) is how bright the screen looks from the audience: the light that comes back from the surface toward the eye.
So the same projector looks dimmer on a bigger screen (the same lumens spread over a larger area), and a screen with gain sends more light toward the viewer than a plain white one.
The formulas
- Illuminance (lux) = lumens ÷ screen area (m²). The result is the average over the whole screen.
- Luminance (nits) = illuminance × gain ÷ π. This assumes an ideal diffuse screen, which looks equally bright from every direction. It is an approximation, not a standard formula.
- Foot-candles = lumens ÷ screen area (ft²) = lux × 0.09290304.
- Foot-lamberts = foot-candles × gain. A foot-lambert is defined as 1/π candela per square foot, so for an ideal diffuse screen the π cancels out and the result is exact.
The screen area is calculated in square meters first. The conversion to square feet uses the exact definition 1 ft = 0.3048 m, so 1 ft² = 0.09290304 m². The two units of luminance agree with each other: 1 fL = about 3.426259 nits. NIST lists 1 footlambert as 3.426 259 cd/m² and 1 footcandle as 10.76391 lux (neither is marked as an exact factor).
Screen gain
The gain says how much brighter than a reference white diffuse surface the screen looks when viewed from the front. A gain of 1.0 is the reference. A higher gain makes the screen brighter in the main viewing direction and usually narrows the angle from which it looks bright. The gain is a number from the screen's maker; this calculator uses it as a simple multiplier.
Example
A projector rated at 3,000 lumens on a screen 2 m wide and 1.125 m high (16:9) with a gain of 1.0:
- Area = 2 × 1.125 = 2.25 m²
- Illuminance = 3,000 ÷ 2.25 = 1,333.3 lux = 123.9 foot-candles
- Luminance = 1,333.3 × 1.0 ÷ π = 424.4 nits = 123.9 foot-lamberts
The same 3,000 lumens on a screen of 16 ft × 9 ft (144 ft², about 13.4 m²) gives about 224.2 lux, 20.8 fc, 71.4 nits and 20.8 fL.
Notes
- Catalog lumens are a nominal value. The measurement method matters (ANSI lumens, and other methods that give different numbers). Lumens measured under different conditions cannot be compared.
- Ambient light is not included. Any light in the room adds to the screen and lowers the contrast. The estimate is for a dark room.
- A real screen does not look equally bright from every angle, and the picture is brightest at the center and dimmer toward the edges and corners. The result is an average.
- The lumens can be 0 or more, with up to 7 digits before the decimal point. Sizes must be greater than 0. The gain must be greater than 0 and at most 100. The screen size can be entered in m, cm, mm, in or ft.
- To plan the distance between the projector and the screen, see the Projector Throw Distance Calculator. To find the width and height of a screen from its diagonal, see the Screen Size Calculator. For how light weakens with distance, see the Illuminance Distance Calculator.
Frequently asked questions
What is a foot-lambert?
A unit of luminance used mainly in North American cinema and display work. One foot-lambert is defined as 1/π candela per square foot, which is about 3.426 nits. For an ideal diffuse screen, its value in foot-lamberts equals the illuminance in foot-candles times the gain.
Why are the nits and the foot-lamberts different numbers?
They are different units for the same brightness. Multiply foot-lamberts by about 3.426 to get nits.
Does a brighter projector always give a brighter picture?
On the same screen, yes. But a larger screen spreads the same lumens over a bigger area, so the picture gets dimmer as the screen grows. Screen gain and ambient light also change what you see.
Why does my measured brightness not match the result?
The calculator assumes an ideal diffuse screen in a dark room and takes the catalog lumens at face value. A real screen, the projector settings, the lamp or laser age and the room all change the measured value.