What's wrong with the current approach
- The m^2 area in the definition of illuminance (lm / m^2) is the area receiving the flux, not emitting it. Therefore, using the total area of the monitor in your calculation is incorrect. (Instead it should be the area of the detector used.)
- Luminance (cd/m^2, or lm / sr / m^2) is not the amount of light reflected from an object, but rather the flux (lm) through both a direction (sr) and a projected area (m^2).
- The assumption that the measured illuminance unit of lux is directly equal to a luminance unit of nit (a unit interchangeable with cd/m^2) is incorrect.
A better approach
Let's continue to place the illuminance meter directly against the monitor. This will make the area of luminous emittance/exitance the same area as that of the illuminance detector. (Commonly, this is a 1 inch diameter circle, or π * (25.4 mm / 2)^2 =~ 161.3 mm^2 = 0.0001613 m^2.) For now let's just call this area A.
The general plan: calculate total flux that reached the detector. Then use that total flux (and some assumptions) to calculate a luminance that would result in the same total flux leaving the monitor. Again, we will use the area A to denote where the flux leaves the monitor and enters the detector.
To make the math easy, we shall assume the monitor is a Lambertian emitter: that it emits the same Luminous Intensity in all directions. (Of course, this is almost never true in practice.)
Step 1: calculate total flux reaching our detector.
Since lux = lm / m^2, where the m^2 is our detector area A, therefore the total flux reaching our detector is lm = lux * m^2, or 650 * A.
Flux (lm) = 650 lm/m^2 * A m^2 = 650 * A
Step 2: relationship between luminance (of Lambertian emitter) and total flux leaving an area
Per Lambert's Cosine Law, the luminous emittance of a Lambertian emitter is related to luminance by:
Emittance (lm / m^2) = π * sr * Luminance
Or, put another way:
Luminance (lm / sr / m^2) = Emittance / π / sr
Step 3: final luminance calculation
Assume all the flux emitted through our area A is captured by the illuminance meter. Therefore, the emittance is flux / A, or (650 / A) * A. (The area cancels!)
Leaving us with:
luminance = emittance / π / sr = 650 / π =~ 206.9 cd/m^2
206.9 cd/m^2 - That's pretty close to your original number. This is a coincidence, as the monitor area you used happens to be very, very close to 1/π.
Why doesn't my 'measured' luminance match the rated luminance?
Often manufacturers rate their devices on the 'best' specs that can be achieved, rather than 'typical' performance. Best guess? Either your monitor or the device driving it is not configured to give you the maximum achievable luminance. A review of this monitor mentioned they could not measure the maximum rated luminance of 300 cd/m^2, either.
It fell slightly short of its 300-nit (candelas per meter squared)
rated luminance, doing best among our standard modes in sRGB, where I
measured it at 265.9 nits.
Note the reviewer had to configure the monitor to its 'sRGB' mode to get the highest luminance.
Final comments
Because of our assumptions, this is not a recommended approach if you care about accuracy. It's very possible that the assumption of a Lambertian emitter is too risky, and contributes in a significant way to the deviation from the expected value of 300.
Now can I scold you for trying to use an illuminance meter to measure luminance? ;)
