## Lifecycle Costs of Lightbulbs

Scientific American had an article on the costs of light bulbs1. I wanted to figure out a way to fairly compare the rough lifecycle costs of the bulbs to the consumer. I figured the best way to do that would be to determine the cost per an operating lux-hour.

We’re going to figure out the cost to buy and operate lights that emits 1600 lumens for 20000 hours $(3.2 \times 10^{7} lm \mbox{-} h)$ given that energy costs $\0.085\ kWh^{-1}$2:

Cost of energy: $\frac{100 W}{1600 lm} = 0.0625 W \cdot lm^{-1}$ $0.0625 W \cdot lm^{-1} \times \0.085 kW \mbox{-} h^{-1} = \5.313\times 10^{-6} lm \mbox{-}h^{-1}$ $\5.313\times 10^{-6} lm \mbox{-} h^{-1} \times 3.2 \times 10^{7} lm \mbox{-} h = \mathbf{\170.00}$

Cost of bulbs: $\frac{\0.37}{750 h} = \4.933\times 10^{-4} h^{-1}$ $\4.933\times 10^{-4} h^{-1} \times 20000 h = \mathbf{\9.87}$

Total Cost: $\170.00 + \9.87 = \mathbf{\179.87}$

You can do the same math for the rest of the bulbs (substituting the proper numbers in) to get a chart that looks like this:

Incandescent
Halogen
Incandescent
Compact
Fluorescent (CFL)
LED
Watts (W) 100 77 23 20
Lumens (lm) 1600 1600 1600 1600
Cost/bulb $0.37$1.59 $2.23$45
Life span (hours) 750 1000 10000 20000
W/lm 0.0625 0.0481 0.0144 0.0125
$/(lm-h) 5.313E-06 4.091E-06 1.222E-06 1.063E-06 Cost to run$170.00 $130.90$39.10 $34.00$/h 0.493E-04 1.590E-04 2.230E-04 2.250E-04
Cost to buy $9.87$31.80 $4.46$45.00
Total cost $179.87$162.70 $43.56$79.00

Here’s the thing I found amazing: there’s a big push to implement LEDs, probably because of the ‘cool’ factor. However, they don’t save that much more energy over CFL — about 13% — and they cost almost twice as much to operate right now. Manufacturers are going to have to have to drop the cost of LED lights a lot in order to make a change worth it…or the government will have to ban mercury in lights3.

Graphic by George Retseck and Jen Christiansen
Sources: U.S. Department of Energy and Efficacy calculations based on currently available bulbs (traditional, halogen and compact fluorescent); SWITCH LIGHTING (led)

1. How to Buy a Better Lightbulb, John Matson, Scientific American, January 6, 2012

2. CFLs contain about 4mg of Mg, per Energy Star