# Understanding Watt hours, Amp Hours, Amps and Volts

First off lets start with the definition. Watt hours are a unit of energy, usually electrical energy, equal to the work done by a single watt acting for one hour. This is also the equivalent of 3600 Joules. In order to calculate Watt hours you need to do some multiplication. First off you take the Watt rating of the product and multiply that by the amount of time used in hours. A 40 W bulb will use 120 Watt hours over a period of three hours.

Understanding Watt Hours

This gives you the most basic understanding of watt hours. Watt hours are the most important unit of measurement when looking at a cordless electric lawnmower. The unfortunate thing is that most manufacturers do not supply a consistent rating system that matches other manufacturers. If everyone were using watt hours it would be easy to tell which lawn mower had the ability to complete the most work before running out of battery power.

## Intro to Watt Hours

What I’m going to do with this post is a little bit different than anything else I have done. Usually I will go through all of the research I’ve done and rewrite a post in my own words. This topic however is a little bit more complicated and I’m going to leave a link to each of the sites where I took the information that I will be sharing with you. I am still waiting for permission from 2 of the sites so I had to add my shortened rendition. First I would like to say to be sure and take a look at the extension cord PDF that is linked at the top of this page. Even if you’re looking at a cordless lawnmower which would be the reason you’re interested in watt hours and watts etc it’s good to take a look at that PDF because it has a good explanation of amps, watts and volts.

I will make these next three sections in italics divided by a line of dashes. The link for each will be at the beginning of this section. After these three sections there will be a video and couple of other links if you want to do more reading about the subject. —(Return to Top)
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## Synopsis – Electric Car Forum

My original intention was to post the entire article from the other site into this section. However I’m awaiting response from the owner of the site so we can post it here with their permission. In the meantime I encourage you to read my synopsis here as well as visiting the site and reading the information from there. I will be adjusting this link so that it opens into a new tab or a new window. So if you click on the link and you don’t see anything look around for a new tab or window. First off the equations for conversion of Watts amp’s and volts are as follows:

Watts = Amps X Volts
Amps = Watts / Volts
Volts = Watts / Amps
Watt-Hours = Volts X Amp-Hours

On the site I got this information from the original poster used a very good analogy of a ski resort. So if your electrical system was like a ski resort with chairlifts and skiers it would work something like this. The voltage of the system would be comparable to the height of the chairlifts. This would mean the higher chairlifts went the more potential energy the system would have. Suppose you had 10 chairlifts at 12 Volts each. If you put them all in a row up the hill you would have 120 Volts. Or you can have them all next to one another and other and you would only have 12 vollts. Remember Volts is the potential.

For this little scenario lets say that the amps are the number of skiers in the system traveling up and down the mountain circuit. So when you put all the lifts in a line one after another they go way up the mountain. You can get a limited number of skiers per lift, lets say one per lift and call that 1 amp. They can go way up the mountain but only one at a time can get off. However if you put them all side-by-side you have fewer volts, because you don’t go as high up the mountain, but you would have 10 amps because 10 skiers could get up to the top of the lift at the same time.

Batteries are like the chairlifts. They add energy to the system taking the skiers up the hill. The power consumption of your motor is like the energy used when coming down the hill. That energy that was used to bring the skiers up is then used up on the downward travel. Follow the link at the beginning of this section to go read the entire article.

### Water analogy

In this article they also use the water analogy. That is also available in my extension cord PDF that is linked at the top of the site. Voltage in this analogy is a measure of potential. So in the water analogy voltage is similar to water pressure. In the water analogy amps is equivalent to water flow or volume of water. Watts or the rate of power delivery much like the power in a water mill so is water falls from a higher fall more volts it will produce more power than the same amount of water from a lower fall so a high volume of low pressure water will spin a mill the same amount as a fast or high-pressure amount of water and a lower volume.

With these inputs that is how you get Watts is equal to the Amps times Volts. So you need to specify how much (what power level) and for how long. With water if you increase the pressure in the pipe the flow will increase and your power also so if you increase the pressure (the voltage) you can deliver more water (amperage) with a smaller pipe. This is why transmission lines for moving power over long distances is done at extremely high voltages. Visit the link at the top of this section and read the PDF for extension cords for a better understanding.

This means that if you have:
2 12v 10ah batteries in series make for 24v 10ah.
2 12v 10ah batteries in parallel make for 12v 20ah.

It ends up being the same amount of watt-hours (multiply volts and amp-hours to get watt-hours). —(Return to Top)
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## Calculating battery Watt Hours

Battery capacity is usually listed in amp hours. Sometimes it is listed in Watt hours. You need to know the voltage of the battery and the current draw of the device used to be able to calculate the life of the battery. The other thing that you need to also consider is that you should never drain a normal battery much more than 50% as it shortens its life. So let’s look at some different scenarios. Say you have a 5 V battery with a 20 W hour rating and you’re using 2 amps of current, then the Watts delivered by the battery equals 10 W 5 V light to amps therefore this battery would last for two hours, technically. But saying it would last two hours means you drain the battery completely so if you use this calculator at the link above remember you should then take your final number and divided by two because you don’t want to drain your battery completely.

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## From a Remote Controlled Forum

### Amp Hours Vs Watt Hours

I actually received permission to post this in full. No need to visit the site unless you are just curious.

Many times in the RC hobby the measurement of Amp hours or milliamp hours is given close attention. Amp hours (AH) is essentially the capacity of the battery. A better evaluation of the batteries capacity is given by the “Watt Hours” it provides. The only difference is that watt hours also takes into consideration voltage. Why does this matter with RC Cars and trucks? For one, because you may be using multi voltage packs in your vehicles: the most common two being 7.4 and 11.1 volt packs. If you’re curious which pack is going to have the longest run time you can’t just look at the milliamp hours. You have to take into consideration the total energy- the watt hours.

Luckily the math is easy. You just take the AH on the battery and multiply them by the voltage.

### Two Packs with different Voltage

So if my first pack is a 7.4v 3300 mA battery and the second is a 11.1v 2200 mA battery which one is going to give me a longer run time if I run them both the same? Let’s see…
3.3 x 7.4 = 24.42 Wh
2.2 x 11.1 = 24.42 Wh
Turns out in these to batteries have the same capacity in watt hours.

### Watt Hours for Charging

In this case I’ve got the 12v 22 AH jump starter battery I use to charge all my other batteries and my 2 MaxAmps 7.4v 4000 ma/hour or 4 AH battery.
22AH X 12 V = 264 Wh
2×4 AH X 7.4 V = 59.2 Wh
So you can see if I didn’t take into consideration energy lost in the charging process I could charge my 2 packs about 4 times before depleting all of the energy in the packs. In reality you don’t ever really want Lead Acid batteries to go below even 50%. So I shouldn’t charge this pair of batteries more than twice before charging the large battery.

### Watt Hours for Energy Cost

Now here we are getting to be rather nerdy. If I take into consideration that I drain about 8 AH of battery every time I run my Emaxx, I can easily figure out how much it costs.
8 AH x 7.4 = 59.2 Wh
1 kwH = 1000 Wh
So doing the math by just moving the decimal 3 places I find that running the truck uses .0592 kwH of energy, it will take me about 16 runs to even use 1 kwH which runs about 13 cents around here. So know you know how much it costs to run your remote control car! —(Return to Top)

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