# Lightbulb Challenge: LED vs. Halogen

[Update: See the bottom of the post for a quick update thanks to some issues pointed out by Nicolas Marmet in the comments.]

[Update 2 (1/26/2014): I added graphs for the cost per hour instead of the cost per day assuming 3 hours of use per day. I s'pose it would've made sense to just start with these graphs. Oh well.]

In the 1960s Walter Mischel performed studies involving preschoolers and marshmallows. The "Marshmallow Experiment" involved sitting kids in a bare room and setting a marshmallow1 in front of them, then telling the preschoolers they could either eat the marshmallow now or wait 15 minutes. If they successfully waited 15 minutes then they'd get a second marshmallow to enjoy in addition to the first.

In addition to telling us something about deferred gratification, it's also immensely fun to watch preschoolers in agony attempting to defer their gratification:

This past week I needed to pick up two new lightbulbs for our oven hood. I noticed our local big box home supply store had a fancy new LED bulb that would fit into the outlet. On the downside the LED cost $32.98 compared to$7.98 for the same type of halogen bulb that just blew out. Wow. $32.98 feels really expensive for a lightbulb. I decided to get one of each then do a little cost analysis when I got home. Here are the vitals for each bulb (according the packaging): Halogen Bulb LED Bulb Power 50 Watts 7 Watts Lifetime 2,500 hours 25,000 hours Let me assure you our old halogen bulbs didn't last nearly as long as 2,500 hours. I'd roughly estimate those bulbs are on an average of 3 hours a day. The halogen bulbs should have lasted about 2.25 years at that usage. This is the second time I've had to replace these bulbs and we've only been in our house 3 years. Does this mean the LED bulb will have a shortened lifespan as well? I don't know. I'll cut the bulb makers some slack this post and assume their numbers for the lifetime of the bulbs is accurate. ### How long before the LED pays for itself? The LED bulb uses about one-seventh less power and has 10 times the lifespan of the halogen bulb. It seems pretty clear that at some point it'll eventually pay for itself. But how long will that be? Days? Years? Decades? I hunted down a bill from the electric company and added up all the government surcharges, distribution rates, and so on. Hmm...it seems like they should print the total rate you actually pay instead of only listing the seven different surcharges individually. It'd certainly make it quicker to see what you're paying. Anyway, I pay$0.15373 per kilowatt-hour. What does that mean? It means that if I leave a 1000 watt lightbulb on for 1 hour, it'd cost me $0.15373. Knowing that, I can figure out how much it costs me to keep the LED and Halogen lights on for 1 hour: That's nice to know, but the time has come to make a chart: You might be wondering why the data points jump every so often on the graph. Let me explain: The halogen bulb line jumps$7.98 after every 2,500 hours of use. Why? That's the bulb burning out and me running out to the store buying a new bulb for $7.98. You'll notice the LED cost jumps$32.98 after 25,000 hours of use. Same deal.

I added in best-fit2 lines and had Excel whip up the equations for those lines. The trendlines' slope is the cost per day (assuming the bulbs are on 3 hours a day). I'm really interested in the intersection of the two trendlines. It's at that point where the LED bulb is actually saving me money. We can see they cross just before 1000 days. We can do better than that. If I subtract the two equations from each other, I should get an equation that gives the difference in cost between the two bulbs:

### A related student activity

It seems that many sustainable technologies (LED bulbs, electric cars, photovoltaic cells) require more money up front. Over time, just like the LED bulb, they generally pay for themselves. Have students investigate whether these extra costs pan out by having them pick a sustainable technology (like buying an electric car) and by doing some research into, for example, their family's driving habits. After a few calculations they can determine how long it would take for the electric car to pay for itself compared to an equivalent gas-powered car. Open up the topic to students- let them pick topics that interest them. Have them do additional research into the costs and benefits beyond just dollars and cents. Encourage them to interview people who have already implemented these changes. Most of all, let them take the time to puzzle over how to figure this stuff out. Be there to help and guide them, but please, please, don't just give them worksheet that has them plug in some numbers to get some type of answer.

#### UPDATE

Nicolas Marmet (in the comments) pointed out a few things that I think are worth addressing, primarily the issue with not continuing the data in the chart above for several lifetimes of the LED bulb. I didn't think there would be much effect, but just because I was curious, I made a new chart (below) that goes through 11 lifetimes of the LED bulb:

As you can see, the slope of the best-fit line jumps from 0.0042 dollars/day to 0.0070 dollars/day. While that's still significantly cheaper than the Halogen bulb (at 0.0319 dollars/day), it's different enough that some new calculations are in order. After updating the Savings equation (from above), the new equation looks like this:
$\text{Savings}=\ 25.00 - 0.0249x$

This tells us that it'll take an additional 102 days than the calculation above until the LED is the cheaper choice. It'll take 1004 days, or 2 years and 9 months until the break even point. Not too much longer, but still longer.

Also, a quick run through Nicolas Marmet's other points:

• As far as the difference in lumens between the two bulbs, I no longer have the boxes pictured above, and can't make out any lumens listed on the boxes in the picture above. Qualitatively looking at the lights side-by-side in my house, I don't notice much difference in brightness between the two, and I'd pick the LED as the brighter bulb- though perhaps that's a trick due to the whiter quality of its light.
• I can't say much about the premature failure of LED-bulbs other than to point out that my LED bulb hasn't failed yet- though as of this update it's only been 327 days since being installed, which assuming 3 hours per day of use, is only 3.9% of the bulb's 25,000 hour lifespan, and I'm still 2 years, 10 months, and 8 days away from the break-even point. I'll update this post again once either bulb has failed.
• LED buzzing: The LED I installed doesn't buzz at all. It has made no noises at all that I've been able to perceive. My cats don't act weird (or I guess I should say, weirder than normal) when it's on, so that's not an issue.

While there's certainly a lot of time left where I could be proven wrong, it does still seem over the long-term the LED bulb is a smarter investment, though you're probably not going to be able to retire early from the savings gained from using LEDs.

#### UPDATE 2 (1/26/2014)

Here are two views of the same graphs using Cost per Hour instead of Cost per Day of 3/hr use:

Below I zoomed in to only include the costs up to 3200 hours so the break even point becomes more clear.

So, after 2906.98 hours of continuous use (or 121 days), it becomes cheaper to purchase a 7W LED bulb over a 50W Halogen.

______________________________

1. According to the Wikipedia, Mischel let kids choose whether they wanted a marshmallow, Oreo cookie, or pretzel stick. I guess the "Marshmallow, Oreo, or Pretzel Experiment" doesn't quite roll of the tongue as nicely. (back)
2. I set the y-intercept for the halogen and LED bulbs at 7.98 and 32.98, respectively. Since you're paying that money up front, it follows that at time zero (when you've purchased the bulbs but haven't used them yet) you're already out the cost of the bulb. (back)