# SMD LED: How to calculate optical power (in mW) from luminous intensity (in mcd)?

I chose an LED for my application but I need optical power, in mW.

In the data sheet, luminous intensity is shown in mcd but I did not find formulas for calculation although there are graphs, etc.

Where luminous intensity is 180 mcd and viewing angle 120°, etc.

Please provide any necessary formulae for my case.

I could not find the exact formula on this website.

• This app note provides an overview. thorlabs.de/catalogPages/506.pdf For your monochromatic case it's not too complex. For ballpark you can assume an optical efficiency of ~20% and calculate from the electrical power dissipated. – Mark Apr 24 '19 at 22:12
• How much power do you need 5mW? 50mW? – Tony Stewart Sunnyskyguy EE75 Apr 25 '19 at 1:07
• @Mark, every "source" that claim to calculate emitted optical power (in units of power) from luminosity starts with certain "efficacy" based on different type of sources. Your assumption about 20% is totally arbitrary, I have a UV LED that specifies 54% efficiency. The question is clearly articulated in the title. I believe the luminous intensity can't be translated into "energetic intensity" (aka "radiant intensity") without knowing spectral density of the source, but I am waiting for someone more knowledgeable to provide good concise answer. – Ale..chenski Apr 25 '19 at 2:08
• This question has the same unknown, and therefore the same answer applies: Optical power cannot be computed when the beam dispersion angle is unknown. beam dispersion angle =/= viewing angle (definition wise) – Huisman Apr 25 '19 at 6:28
• I need a SMD LED with optical power of 5-6mW . I noticed that some of you mention an efficiency of 20% (Mark) Thank you for your link . From data sheet we can find : Power dissipation - max. 70mW ; Luminous intensity 180mcd – Patrick19 Apr 25 '19 at 16:48

Okay, let me try to solve this problem.

Parameters: peak wavelength 527 nm, Luminous Intensity 0.18 cd at 5 mA and 2.9 V, emission angle 120 °.

The candela is the luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency 540×10^12 hertz and that has a radiant intensity in that direction of 1/683 watt per steradian.

So 1cd = 1/683 W/sr = 1.464 mW per steradian.

Luminous intensity measures (lm and cd) are linked to human eye sensitivity curve, which complicates re-calculations into optical power. The maximum in light frequency in the above definition corresponds to wavelength of 555 nm, which is pretty close to the green LED emission, so we can ignore the difference along the "Photopic Spectral Luminous Efficiency Curve".

The LED emits into 120°, but if we want to calculate total emission, we need to integrate over all angles, so the "effective" (ballpark estimate) angle for "flat emission" will be about +- 50°. One steradian is +-33°, so the led illuminates an area of about (50/33)^2 = ~2.3 sr. The narrower is viewing angle, the brighter is LED appearance, but the emitted power is obviously the same.

Therefore, the emitted power is 1.464 mW/sr * 0.18 cd = 0.263 mW/sr, times 2.3 sr, or about 0.6 mW total.

The consumed power is 5 mA * 2.9 V = 14.5 mW, and therefore "luminous efficacy" of this LED is about 4%.