## 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.

## math

mcd to lumens,mW:

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

$\mathrm{steradians}=2\times \mathrm{\pi}\times {\mathrm{radius}}^{2}\times \left(1-\text{cos}\left(\mathrm{radians}\right)\right)$ 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

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

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

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

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

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