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# LED MCD to mW,lm to W Calculator

## Overview

in these calculators, W and :mW refers to OPTICAL POWER, not input power.

Calculate works best at the sample points such as 400-700nm in 25nm increments. Spline tries to approximate the other points and fit a bell curve.

This page is essentially here to do as much of the heavy lifting as possible for the user (and speed up their work so they can get their work done).

LED's and many things that emit light typically get dimmed around the edges of the beam. this is what a web page or post said - sorry, I have lost the reference.

## request for conversion equation/math help

I got my questions answered I think.

can someone verify if these numbers that are output are correct, and if not, by what factor? I wonder sometimes.

I still do have questions regarding LED's which are measured in degrees Kelvin + W + beam half angle in degrees, I am not sure how to calculate degrees kelvin into RGB cd or W, if someone finds a page I would appreciate it. If there is someone into Optical Engineering who is willing to help, that would be greatly appreciated! email me here! Then I can rewrite this page so everyone into electronics can use it more, based on data sheets. I know the beam angle will need to be converted to conical steradians. if this is not possible, please let me know. if an approximation is possible, I would like to attempt this.

I did get most all of the math I needed.

updated and corrected calculators with proper (I think) equations 7/27/2013, 10/29/2013

upgraded input to handle SI and IEC prefixes like m in mcd which I code as :m so therefore :mcd or :mW and W is just W 9/10/2013

I don't understand the radius quite yet, it's supposed to be dimensionless, yet it does have an effect on the lumens. I forgot if this is measured in quantity of radius or steradians. my thinking is it's based on 1 radius for 1 steradian, the radius being the distance to the lens from the LED chip say which is about 2-3mm, and you multiply this n number of times to get the distance to the target object, and this n is your distance.

## lm to mW calculator (single-color)

#### results

0 mW, 0 W
0 lm (lumens or luminous flux)

## mW to lm calculator (single-color)

#### results

0 mW, 0 W
0 lm (lumens or luminous flux)

## cd to W,lm calculator (single-color)

OR

#### results

0 mcd, 0 cd
0 mW, 0 W
0 lm (lumens or luminous flux)

## W or mW to mcd or lm calculator (single-color)

OR

#### results

0 lm (lumens or luminous flux)
0 mcd, 0 cd
0 mW, 0 W

## cd to W,lm calculator (RGB - white)

OR

#### results

0 mcd R, 0 cd R
0 mcd G, 0 cd G
0 mcd B, 0 cd B
0 mcd max, 0 cd max
0 mW R, 0 W R
0 mW G, 0 W G
0 mW B, 0 W B
0 mW max, 0 W max
0 lm R (lumens or luminous flux)
0 lm G (lumens or luminous flux)
0 lm B (lumens or luminous flux)
0 lm max (lumens or luminous flux)

## W to cd calculator (RGB - white)

OR

#### results

0 mcd R, 0 cd R
0 mcd G, 0 cd G
0 mcd B, 0 cd B
0 mcd max, 0 cd max
0 mW R, 0 W R
0 mW G, 0 W G
0 mW B, 0 W B
0 mW max, 0 W max
0 lm R (lumens or luminous flux)
0 lm G (lumens or luminous flux)
0 lm B (lumens or luminous flux)
0 lm max (lumens or luminous flux)

## math

mcd to lumens,mW:

$\mathrm{radians}=\frac{2×\pi ×\mathrm{degrees}}{360}$ OR radians=2*π*degrees/360

$\mathrm{steradians}=2×\pi ×{\mathrm{radius}}^{2}×\left(1-\text{cos}\left(\mathrm{radians}\right)\right)$ OR steradians=2*Math.PI*radius^2*(1-cos(radians)); this is for a spherical cone

$\mathrm{cd}=\frac{\mathrm{mcd}}{1000}$ OR cd=mcd/1000

$W=\frac{\mathrm{mW}}{1000}$ OR W=mW/1000

$\mathrm{mcd}=\mathrm{cd}×\mathrm{1000}$ OR mcd=cd*1000

$\mathrm{mW}=W×\mathrm{1000}$ OR mW=W*1000

$\mathrm{lm}=\mathrm{steradians}×\mathrm{cd}=W×\mathrm{luminousEfficiencyInLumensPerWatt}$ OR lm=steradians*cd=W*luminousEfficiencyInLumensPerWatt

$W=\frac{\mathrm{lm}}{683.002\text{lm/W}×\text{luminousEfficiency}\left(\mathrm{wavelength_nm}\right)}$ OR W=lm/(683.002lm/W*luminousEfficiency(wavelength_nm))

$\mathrm{lm}=steradians×\mathrm{cd}=2×\pi ×\left(1-\text{cos}\left(\frac{\mathrm{radians}}{2}\right)\right)×\mathrm{cd}×{\mathrm{radius}}^{2}$ OR lm=steradians*cd=(2*π*(1-cos(radians/2))*cd*radius^2

###### articles
when it comes to optical power, mW and W is output power, not input power.
articles on mw to mcd conversion - hint requires beam angle
google search: beam angle full power (turns out this is a better search than view angle half power)
google search: beam angle full power (turns out this is a better search than view angle half power)
this applies to calculating cd: with this you can generate your own tables, and it's up-to-date. you want the 2 degree, 1 nm, and I *think* it's the Quantal(log). for compatibility with programming languages and convertability, I would suggest the CSV format or XML format - the XML is really hard to deal with right now, there's no good way to read it in a browser to make a web app using jquery - there are no good examples out there and functionality is awful for json and xml.
unfortunately, it's uniform, and LED's are not uniform in intensity, they dim around the edges of the beam. it also doesn't take into account radius (distance). so I guess you could say you should actually put in the curves and diagrams into the calculator and make the calculator work with that, you will end up doing integrals and other stuff to get your optical engineering done is my guess. and it's not going to be a fun trip. I don't see a way to input curves and beam diagrams visually and have it work well with a mouse. you would have to get the data from the mfr. and that's like extracting teeth. the approximation is what I am going to go with due to practicality - if there were just an equation for it, I would put it in and the necessary variables. or lm=(2+-2*cos(deg/2))*cd*π