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Rechargeable Batteries - Yes or No?
TheFifthElephant asks: "I currently use quite a few devices that require various size batteries and I feel horrible just tossing them when they die. I saw a recharger at a retail store today and was thinking to myself how much waste it would reduce by using rechargeable ones. Which units have you used happily and/or which units have you heard of/read about satisfying someone else? Are the more expensive units better? What chemical rechargeable batteries last the longest/recharge the most?"
I'm using NMH batteries for just about everything battery powered in the house nowdays. NiCad's dont last as long and are very bad for the environment. The batteries I have claim to be good for several hundred cycles, which at the current rate is going to be about 30 years ;)
I have an old olympus camera that came with Ni-MH AA batteries and a battery charger ... it has lasted me near 4 years.
Those batteries keep their energy for 3 months at a time easily, when I am not on vacations or otherwise using the camera.
Sig Nazi- "No Sig for you, come back 1 year."
These batteries kick serious booty. In my digital camera, a single charge outlasts even the best disposable batteries by a factor of 2 or 3. In about a year I've already saved more in disposable battery cost than I spent on the charger and cells.
Definitely worth the investment. I have Panasonic brand, but only because that's what they had at Costco. I doubt that there is a big difference between brands of similarly-rated cells.
My amazing wife - Artist, Author, Philosopher - Laurie M
Have had good results with 1800mAh NiMH RayOVac AA-size batteries in cameras with flash. Havne't used them for much else yet. Had less satisfactory results from Radio Shack-brand NiMH ones. YMWV.
I'd have a personalized plate on my car, but "toxic bachelor" won't fit into 7 letters.
I've used all kinds of rechargables, from cheap Radio Shacks and Mallorys, to expensive Sony units. They are all pretty cose to the same, save for newer lithium-ion batteries.
I keep enough batteries in the chargers to replace the batteries in every device at the same time. And it does save an amazing amount of money in the long run. Most of my rechargables last for five to seven years before they stop being able to hold a charge.
The only batteries I have not replaced with rechargables is AAA-size. At that size the rechargables don't hold enough charge to be worth it.
Boobies never hurt anyone. - Sherry Glaser.
NiMH batteries are great but they have the downside of losing charge very quickly "on the shelf" so you can't keep a bunch of charged MiMH batteries ready to use.
RadioShack sells both kinds.
Lithium ion batteries ... uhm, exist but I know nothing about them. They have advantages over NiMH but don't come in the common form factors I mentioned above, and are more expensive.
You know, you can recycle your dead batteries, right? When I worked at Radio Shack a long time ago, we took in dead batteries and sent them off to be recycled. I'm not sure if this was just my store, or a company wide thing, but there are free recycling services out there.... so don't throw them away!
I have been using the iGo Juice to power my Powerbook and peripherals and find it to be quite the appealing solution including charging handhelds and cell phones when I travel. The iPod gets charged through the Firewire port (awesome idea), so other than that, I'm set. All of these devices appear to use Lithium Ion batteries and have decent performance, (especially the Powerbooks).
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For AA batteries, go to Walmart and pick up the NiMH rechargables at 1800mAh and a charger. I think you can get a combo pack (4 batts and charger) for something like $12, which is a heckuva a good deal. These batteries last and last and last.
The 1800mAh batteries are an absolute requirement for digital cameras. Using standard alkalines, I would get just over 30 digital pics in my Toshiba camera. Using 4 1800 NiMH, I get about 200 before needing a charge.
I also use them in my FRS radios and GPS, and they last forever.
I've also used various brands of NiMH's besides the Walmart specials and haven't seen much difference in quality.
You know you're a geek if you've ever replied to a tagline.
NiMH rechargables. You should have no problem finding 1800mAh AA cells, and these hold up quite well to frequent charge/discharge cycles. I've been using them for about 4 years and they can take quite a pounding.
What's even better is that a lot of cordless stuff with NiCads can be converted to NiMH by making your own battery packs. Internally many of the packs are just a few AA cells soldered together.
If you do this, look for places that sell flat-top and soldertab batteries. Some of the cartridge-type battery packs won't fit the normal button-top batteries, and soldering can be hard on the cells if you try to solder directly to the cell itself.
I did this with my Uniden 900 Mhz DSS phone. Before it would go ~90 minutes on a fresh (new and fully charged) NiCad pack. Now I can get over 2 hours of talk time, leave the phone out of the charger over night, and still have it be perfectly usable the next day.
I was concerned about the charging system, but not any more. A friend has done this for a long time (NiCad->NiMH conversions) and hasn't had any problems, and neither have I.
Imaging-resource.com did a great review of a ton of rechargeable batteries. The electronics geek in you will enjoy his breakdown of how he conducted the tests.
C - A language that combines the speed of assembly with the ease of use of assembly.
Da Blog
- Buy a good charger. Cheap ones can fry batteries, take longer to charge, and can go up in smoke easily. Also, make sure it can charge NiMH batteries as well as NiCDs; if you have high-drain devices like digital cameras, then you want NiMHs, and probably don't want to pay for a new charger for 'em. Expect to pay $30-$50 USD for a decent one.
- When you buy batteries, look at the milliamp-hour rating. That's the capacity they can hold: for example, an 1800 mAh AA could supply (theoretically) 1 mA for 1800 hours, 1800 mA for one hour, or anything in between. While mAh ratings do tend to be stretched a bit (the tests are performed under the most favorable circumstances possible), it's the best guide you can get to how long the battery will last in the device you plan to use.
- Don't buy more battery than you need. Your TV remote probably doesn't need expensive 2200 mAh NiMHs, so put in cheaper 800 mAh NiCDs.
- You'll be better off buying online than anywhere else. I've had good luck from several companies, but note that the "Energizer" branded batteries are relabeled and marked-up generics; you can get better batteries, cheaper if you go with other companies.
- Get extra batteries. You should have a few sitting around for when something important goes dead; don't just buy what all your devices need. Get a few extra of each type you use, or just keep alkalines around to use while recharging.
- Don't be too hard on your batteries. Many good chargers have a "fast" and a "trickle" setting; don't use the "fast" setting unless you absolutely can't wait overnight. Fast charges are hard on batteries; once or twice won't hurt much, but repeated fast charges can cause a significant drop in total battery life.
- Finally, if you have some high-drain devices and want to get more battery life, try hacking something onto the AC adaptor. A good guide to doing this with your digital camera is here; the principles are pretty much the same for anything else that has an AC adaptor socket.
Good luck!That's it. I'm no longer part of Team Sanity.
NiMH batteries last a factor 2-3 longer than NiCd batteries, are less environmentally unfriendly, and lack the memory effect that made people hate rechargeable batteries in the first place. What this means is that a fully charged MiMH battery will last as long, if not longer, than a regular alkaline battery in the same application. Capacity of batteries is rated in milliamp hours. A penlight rated at 2000 mAh will, in theory, provide 2 amps of power for an hour. It goes without saying that bigger is better.
This guy has tested several dozen different types of NiMH penlights for use in digital cameras. Although there are many other uses for the things, this seems to be one of the more common and at least vaguely representative of what to expect.
When choosing a charger, make sure it supports, and is set to charge NiMH batteries. Running a NiCd cycle on them will yield unsatisfactory results. There are fast chargers available that will charge your batteries in as little as an hour and it's commonly accepted that these don't harm the batteries much.
I want the fire back.
The alkaline starts out at around 1.63 volts and discharges to around .9 volts before it is considered dead. The NiMH is flat at 1.2 volts. For some apps, the NiMH battery comes up "low battery" (like in my friend's pager) because the pager may consider an alkaline discharged to 1.2 volts as about done with. So you have to find out if 1.2 volts per cell will run your appliance.
The other thing about the NiMH is that it self discharges -- it is even worse than the NiCad, only it isn't supposed to have the memory effect that a NiCad has (the camcorder which doesn't fully discharge the NiCad which means the NiCad never ever seems to ever recharge and ever run the camcorder).
Now for the alkaline rechargeable. They say you can put ordinary alkalines in one of those chargers -- tried it and it won't burn the house down, but it won't hold a charge, or it will recharge but have really high internal resistance on discharge. I guess you have to pay for those fancy Renewal batteries if you want to recharge an alkaline.
OK, here's the deal. A fully charged alkaline is over 1.6 volts (none of this 1.2 volt business), and it is supposed to hold its charge forever (I measure .01 volt per day degradation). The rub is that you can't discharge them (ha, ha). What I mean is that if you use them in a flashlight and discharge them until the light gets dim, you have discharged them down to that .9 volt, and you are lucky to get one or maybe two recharges (if that) out of them. The trick is to discharge them only down to 1.5 volts and then freshen 'em up in the charger. Apparently they only like to be discharged a little bit and then recharged as soon as possible -- I use D-cells in a couple of flashlights (a 4-cell Mag and a 2-cell ordinary flashlight). If I use a flashlight on a project (like to change a dead car battery at night, or to poke around a crawlspace, I recharge them as soon as I can). I am told they will live (Rayovac data sheets) nearly forever that way.
There's also this Battery Shootout ranking system, skewed towards small portable electronic device effectiveness.
Da Blog
I recommend a smart charger like the Maha C204F from Thomas Distributing. They have all sorts of batteries at great prices (not affiliated just a happy customer).
This charger also has a conditioner feature that will help bring those older batteries back to life (the ones that you were using the dumb charger on before!).
Batteries that I've charged with this charger last 3x as long in high drain applications like in my GPS unit.
About chargers, understand that there are two types out there; timer controlled and -deltaV controled.
You want the -deltaV controlled, which monitor the voltage on the battery to sense when they're fully charged. The timer controlled chargers, will overcharge the battery, and nothing kills batteries like overcharging.
Now it turns out that for low amp applications, even a simple charger will get enough performance out of the batteries, but for more serious applications such as digital camera, a real charger could tripple the number of cycles you'll get out of the batteries.
Also, watch out for 'micro processor controlled.' While all -deltaV chargers will have that on them somewhere, it may also mean timer controlled (as in there's a micro processor keeping time somewhere).
There was a good test this spring in the Swedish equivalent of Consumer report, but unfortunately it's in Swedish (and you have to be a subscriber). The noteworthy point was that not all -deltaV chargers are created equal, one undercharged, so you may want to check around. Expect to pay serious money for a serious charger. The good ones in the test were $100-$200 in Sweden, you'd pay perhaps 50%-75% of that in the US (I don't really know the battery charger market).
P.S. Use NiMH. Better for you, and no memoy effect. With a -deltaV charger you can easily top them up if you've had them on the shelf for a while (they'll lose their charge in a couple of months when stored).
Stefan Axelsson
NiCd and NiMH have somewhat lower voltage (~1.2v) than alkaline (~1.5v) but they also have a far lower internal resistance so if you short a NiCd/NiMH you can get far more current than if you short an alkaline.
NiMH also self-discharge quite rapidly - several percent/day. In some apps the self-discharge drains the battery faster than the device does. This also makes them lousy for emergency uses unless they are always on charge.
The upshot of this is that if you have a very low draw app like noise-cancelling headphones or a radio-only walkthing then you may want to stick with alkaline as they last weeks to months anyway and the loss of 0.6v (for 2 cells) may cause problems.
You may also want to stick with alkaline for certain very high-draw apps. Some halogen high-intensity flashlight bulbs specifically recommend against using rechargables. They are designed for use with alkaline and without the limiting factor of the internal resistance of the alkaline battery the bulb will pull too much current and burn out quickly.
On the other hand moderately high draw things like digital cameras are perfect for NiMH. The high draw depletes the alkaline to a point that it can't supply enough current in short order - a couple dozen pictures in my camera. NiMH will power it for a couple hundred. Unless your use level borders on "never", rechargables are the way to go for cameras, flash units, handi-talkies and similar devices.
Beware of chargers that recharge pairs of batteries, however. I recently had some old NiMH batteries that I thought were dead (~12 pix per charge). I had been using the Kodak charger that I got with my camera - it charges cells in pairs. Unfortunately if cells are out of balance it doesn't work well.
I bought a PowerX charger and after a couple charge cycles the batteries were working great again - and they are almost 5 years old.
The PowerX has gotten favorable reviews from ham operators and camera buffs. It has two charge cycles so if you don't need a charge RightNow! you can switch to a slower setting to prolong the life of your battery. Also, each battery is on an independent channel so each battery gets an appropriate charge and you won't be driven crazy when you have an oh-so-common 3 battery device. After charging it switches to a trickle mode to keep the battery topped-off. I've only had mine for a couple of weeks but so far it beats the heck out of my old chargers. Comes with a car cable, too.
~~~~~~~
"You are not remembered for doing what is expected of you." - Atul Chitnis
It's too bad the moderators marked this BS informative.
NiCd and NiMH batteries hold their terminal voltage until almost completely discharged too, they are both actually slightly better than Li-ion in that respect. They will also work will at current draws of up to 1C for NiCd and 2C for NiMH with no loss of performance.
The Lithium batteries that can do 2.5Ah @ 3.6 volts in an AA form factor aren't even rechargable.
Jason
ProfQuotes
about 2200(I think) mAh for a AA, compared with the low 1000's range for most Ni-MHs
:)
I've got a bunch of 2100 mAh NiMH AA's, so they're catching up.
They do have the distinct disadvantage of discharging themselves, but it's not a problem at all when you use them as much as I do. They're also good for a lot more recharge cycles than alkaline.
You can if you keep them in the charger.
Not every charger, actually. Check yours to learn wether it has this 'keep alive' feature.
NiCd and NiMh batteries have discharge curves closer to that of a standard Alkaline AA...
But Alkaline batteries have high internal resistance, so they're not terribly useful in high-current devices like my Kodak digicam. That high resistance causes the batteries to heat quickly, and because resistance increases with heat, it gets worse the longer you use the device. The voltage drop across the resistance causes the output voltage to drop, and before long it can drop below a useful voltage. In high-current devices, NiMH and NiCd batteries work much longer than alkaline batteries, in part because they don't heat as much.
This isn't just theory; I've tried alkalines in my digicam, and they don't last for more than a handful of photos, not nearly as long as my usual NiMH cells. So I can use alkalines, but only in a pinch. For low-current devices like a CD player, alkalines may last as long as NiMH or NiCd, but when they're done you have to throw them away.
Rechargable batteries are wonderful things. Like a lot of other /. readers, I have a pocketful of AA NiMH batteries. There are some things you should be aware of with rechargables before you jump into them, though.
(Mostly AA specific)
First, make sure your battery-powered device is rated to handle rechargable batteries. Alkaline AA batteries are nominally 1.5volts. "Fresh" batteries will probably test to 1.56volts in a digital multimeter. NiMH AA batteries are nominally 1.2volts, and will usually test as 1.26volts freshly-charged. If your device has a voltage meter (if it shows "battery power remaining" it does) then you need to be sure it can handle running with the different voltage. My old family-band radios (some motorola model, don't remember which) were made assuming alkalines at 1.5volts, and gave noticably less powered-on time with NiMH batteries than with Alkalines. The batteries still had juice in them, but were putting out a slightly lower voltage than the radio wanted, and the radio turned itself off.
Second, all rechargable batteries (except possibly lead-acid/gel-cells) have a normal charge cycle rating. This means, effectively, that they can be recahrged that many times, and then they stop holding a charge, the chemistry inside breaks down after that many charge cycles. By chemistry:
NiCad = 500 charge cycles.
NiMH = 400 charge cycles
Lithium Ion = 350 charge cycles
After you recharge them that many times, expect them to become noticably less useful. This is part of why laptop batteries are only warranted for a year, incidentally... 350 charge cycles, 350 days of charge/discharge (about a year), and you have a battery that doesn't last nearly as long as when it was new. This is also why people that buy laptops like intelligent chargers, and don't recharge immediately upon reconnecting to a wall regardless of charge remaining. Recharge based on charge % remaining, and the battery lasts a lot longer, so wait until the battery gets below, say, 85% charge, and it will last 2-4 years instead of one. Intelligent chargers in laptops will check the charge remaining automatically, and only charge when it drops below a given threshold.
Third, you have different self-discharge rates with different batteries, aka, the shelf life. Alkalines are really good here, they have a quite long shelf life, usually measured in years.
NiCads are less good than alkalines, and especially with the multi-cell NiCad packs where you are concerned with polarity reversal, you want to recharge your NiCads every few months, to keep the charge level above a certain minimum where one cell in a pack might get too low, reverse polarity, and basically kill your multi-cell battery pack.
NiMH batteries self-discharge at about 1-2% per day. Yes, a "freshly-charged" battery that is left on a shelf for a month will be down by 25-50% charge. This is environment dependent, of course, varying with temp and humidity mostly.
Lithium Ion batteries have about the best shelf-life of rechargables, about the same as NiCads, really. Still nowhere near alkalines, though. (Again, leave your laptop sitting on a shelf for 3 months, you'll probably have a dead battery. Be aware, and plan accordingly.)
With all this said, I still love rechargable batteries, and use them whereever they fit the device specs.
Oh, and fair warning, if you travel outside the US. Most of the cheap NiMH chargers you see in Walmart and everywhere else are US voltage only, they work with 110V 60Hz AC ONLY. If you are travelling anywhere outside the US and Canada, get an international charger, that can handle 50/60Hz and 110/120/220V. You'll be much happier, and not unpleasantly surprised when your charger gets very very warm and then suddenly stops charging. Bear in mind that the carribbean, while very near the US and supposedly US power specs, has crappy power regulation on wall plugs, and you'll want an international charger there too. Just another thing to be careful of.
This is my sig. There are many like it but this one is... Oops. Frank, I've got your sig again! Where's mine?
-Matt
I replaced over 100 batteries used in our household (three daughters, geek father) with NiMH. No problems at all. I get the next to highest mAh rated batteries from Thomas Distributing (just a happy customer) and I use an Altek 5798 charger. The tri-state LED's give a good status on when its done charging.
I had a few go bad over the past few years, but I know several sets have had hundreds of charges.
The last AA set I got were 2000 mAh and they are great in my Fuji digicam.
www.thomasdistributing.com - don't let the 'web designer on acid' interface bother you, they have always had the best price and reasonable delivery. I even like the 'free gifts' (synth chamois car cloth, plastic battery holders).
Hope this helps!
Radio shack has a nice page about different batteries.
- The voltage drop of the LED is unrelated to the voltage of the battery; the battery voltage just needs to be greater than the drop across the LED for the LED to light.
- For a given brightness of LED, the current needs to be the same; it wouldn't be enormous for a higher voltage. In theory, the LED is a short circuit anyway, to the current is whatever the battery can put out regardless of voltage (at least for the split second until the LED fries.
- There is a current limiting resistor in series with the LED, which according to Kirchov's voltage law has the rest of the voltage dropped across it. So in that case, you know the resistance and voltage dropped across the resistor, therefore you know the current through it, and by Kirchov's current law, you know the current through the LED.
Now, it should be fairly obvious that the larger the voltage dropped across the resistor, the more stable the current will be against slight changes in battery voltage. Therefore, you want a relatively large voltage potential dropped across the resistor (at least as much as across the LED) to keep the current stable. That means the voltage of the battery should be at least double the voltage drop of the LED.Jason
ProfQuotes
2) "Disposable diapers"
Need I say more?
Yes you do. What is a bigger problem for the millions of people living in LosAngeles: Disposable diapers or the lack of drinking water due to a million cotton diapers a week needing washing?
Standard disposeable alkaline batteries have very good capacities but also high internal resistances, so they don't do well in high-drain applications.
NiCD batteries have lower capacities than alkaline, but they have miniscule internal resistance and can push an unbelievable amount of current. I'm getting about 45 amps of current from 1700 mAh NiCD battery packs in one of my RC planes. These batteries deliver close to 100% of their rated capacity even at insane drain levels like this. Downside to NiCD's is that they discharge at about 1%/day, so they are useless for stuff like clocks and calculators, etc.
NiMH have almost the same capacity as alkaline and almost the same internal resistances as NiCD. They are sure to replace NiCD since some new high-drain types can equal NiCD performance. These also self-discharge pretty fast.
Li-Ion are a completely different chemistry. Alkalines push 1.5v/cell. NiCD and NiMh push 1.2v/cell, which is close enough for drop-in replacements. Li-Ions are 3.6v/cell, so they are not really practical in replacing 1.5v alkalines. Li-Ions oxidize over time, so they lose capacity. Useful life for something like a laptop battery is 2-3 years or somewhere around 300 cycles. Li-Ions lose efficiency very fast as current draw increases.
So, to sum things up:
In clocks, calculators, smoke detectors and other long-run, low-current devices, use alkalines.
In high drain devices like digital cameras, flashlights, electric motors, NiMH are probably the best bet.
For insane current draw, use NiCD. Sanyo R-cells can push > 100 amps!
Use lithium only in devices designed for it. A NiMh/NiCD charger can and will explode a Li-ion.
Good luck.
Is operating temperature a concern? NiMH batteries are not so good in low temperatures, so don't use them in a GPS on your Everest Expedition.
What about space/weight/charge density? Lithium Ion batteries have a higher energy density than NiMH and NiCads, but they require more intelligent (read: expensive) chargers, as they are often microprocesser controlled.
Current Drain? NiCads can deliver more current than NiMH batteries.
Access to power supply? Weight and size of chargers? NiCad batteries are the easiest (after Lead Acid) to recharge, so the charger could be lowcost and small sized. You can charge a NiCad quite well with just a dc power supply and an appropriate voltage dropping resistor, just make sure that you time the charging to match the capacity. You can't jury-rig chargers for Li Ion batteries and you have to be very careful for NiMH cells (you really need to detect the voltage drop these guys display when nearing charge completion and trickle charge from that point onwards).
Also, contrary to what others have posted, not all batteries of the same kind are created equal. Stick to name brands (Sanyo batteries have been very good for us) - they tend to last a little longer. Maybe they have more pure electrolyte or electrodes?
Avoid rechargable alkalines. It will end in tears.
Good luck with your decision.
"The big question in our lives is how to be at the same time a hedonist and in a hurry" - Alain Ducasse (?)
A great deal of the raw materials for NiMH batteries comes from China (and Russia), regardless of what the "made in ..." sticker says. (See http://ovonics.com [ECD, the NiMH patent holder] for more info.)
:)
So, if you buy NiMH, you don't have a lot of choice in the matter. This is NOT to suggest avoiding NiMH, which is a superior battery in many situations - just to inject a note of realism.
As for the original poster's question, surely there is a website out there with vast amounts of statistical data on the various brands (and types!) of batteries?
I like NiMH as it is relatively easy (and safe) to recycle. However, keep in mind that NiMH can lose up to 2% of its charge per day sitting on the shelf. NOT a good choice for that emergency flashlight.
If you're not living on the edge, you're just taking up space!
4) Actually, you need a "push mower" like the old days. Save money and slim that fat ass of yours.
Actually, I have a "push mower" (it's called a reel mower) like the old days. It's actually lighter to push around than a regular gas mower since there's no engine, with the added benefit of getting to experience the "fresh cut grass smell" the entire time rather than only after you're finished. The only downside is that you can't let your lawn get out of control. You have to keep up with it because the mower won't cut grass that's longer than four inches or so.
More than you ever wanted to know about battery tech. Keep an eye on the emerging Lithium Polymer batteries @ roughly 3X the current NiCd and NiMh power/weight and power/size batteries. I use them in my micro R/C helicopter instead of the oringal NiMh and get 3X the run (was 5 now 15 minutes) with less than 1/2 the original battery weight (1.75oz vs 3.75oz). These are gonna be cost effective in the next 10 years or so, making a 100 mile range EV very easy and cheap. This is what they are using in the current solar racers. Environmentally friendly as well! Oh the original question? 2000mah NiMh all the way.
Why is this modded funny? There really is a monster brand of battery.
Someone's already linked to one of my pieces about batteries, so I need only pimp Dan's Quick Guide to Memory Effect, You Idiots :-).
Panasonic is (as far as i know) the largest maker of battery cells in the market. They make excellent LiO and NiMH cells. NiMH are probably the best bang for the buck, as they are a direct replacement for regular alkaline batteries. Lithium are great if they will work in our device as they are lighter, and wont be destroyed if you accidentally let them heat up or get too cold. Down side is LiO cost a lot more.
So now I just buy regular alkaline and recharge them until they start leaking, then throw them out. Recharging before deep discharge gives the longest battery life for alkaline. I had a set in my RC car that I recharged after every play session, and they lasted for two years (with several sessions a month).
If batteries leak badly, I clean up the discharge with white vinegar and baking soda.
The amount of water used in the process of makeing diapers exceeds the amout of water when you wash diapers (if you fill the machine up). The a weight of garbage from one average kid using diapers is 1000kg. The energy from transporting the garbage, makeing the diapers and transporting the diapers to the shop exeeds the energy to clean the diapers by serveral times. An average kid uses 5000diapers. That is about $1500. A set of cloth diapers costs about $35. We have used cloth diapers for both our girls. It was really good and as they feel that they are wet when they pee, they stopped using diapers a lot sooner then the other kids at kindergarden.