# Convert Watt to Ampere-hour for battery

I'm trying to find replacement batteries for my UPS, I checked my local store and they dont' have this particular model I need so I'm looking for other brand that does exactly the same. What I usually see on the battery label is something like 12V 7Ah or 12V 9Ah. However, this one is 12V 21W. Does anyone know how can I convert the 21W to the equivalent Ah? Also, what is the reason of specifying the spec in Watt rather than Ampere-hour?

Below is the spec sheet of the battery in my UPS:

http://www.csb-battery.com/upfiles/dow01320199011.pdf

-
The 1.75 Ah that clabacchio's calculation produced is the EFFECTIVE or real world Ah as opposed to what you'll see on the rating plate. Lead Acid Ah are often specified at something like the C/10 (ie 10 hour) rate,so the stated 4C rate gives the battery a much harder time and you get a MUCH lower delivered Ah. It's 2.83Ah rated at 90 minutes. It's probably a 3.5 Ah battery at C/10. It weighs ~= 1.8 kg apparently. A moderate guide to what the new one should be sized. Larger is unlikely to hurt. Look at the curves of lifetime under various conditions and choose one which is not notably inferior – Russell McMahon Feb 19 '14 at 10:33
Thank you every for the input, you all have been a great help! – chmod Feb 19 '14 at 14:31

W is a measure of power, therefore it's likely that it's rated in Wh (Watt-hour, energy).

Since Ah represent a charge (current * time) you can multiply it by the voltage to get Wh; conversely, divide the Wh by the voltage to get the Ah rating.

Looking at the datasheet, there seem to be a reason why a single Ah value is not specified: it varies depending on the load current (see table in the bottom).

The 21 W indicates that it can provide 21 W for 15 minutes (21/4=5.25 Wh) when the cell voltage is at least 1.67 V, times 6 cells means 10 V. This voltage is the minimum tolerated value, and influences the depth of the discharge and, in the long term, the lifetime of the battery.

If you look at the table, the battery is approximately 4 Ah.

-
So if I divide 21W by 12V, I get 1.75Ah?? Isn't it a bit low? – chmod Feb 19 '14 at 10:14
If you divide W by V you gat A, not Ah. It's the rated current. Check the answer again for edits. – clabacchio Feb 19 '14 at 10:27
Thank you for the edit, now I understand how this works. – chmod Feb 19 '14 at 14:27

Here's what it says in the detail of the spec: -

Look at the top table - move along to the 60 minute column - to discharge each cell to 1.85V the current is 3.97A. To discharge each cell to 1.60V, the current is 4.02A.

This makes it a 4Ah battery to me irrespective of the number of series cells - terminal voltage will drop from about 14V (fully charged) to about 9.6V

-
Thank you! you have made it very clear, I wish I can mark you as answered as well. clabacchio came first so I gave him. Hope you don't mind. – chmod Feb 19 '14 at 14:30

Does anyone know how can I convert the 21W to the equivalent Ah?

You can't, they are not equivalent.

• 12V 7Ah is a measure of available energy
• 21 W is a measure of power (energy per second)

21W @ 15min-rate to 1.67V per cell @25°C (77°F)


I suspect that means it can provide 21W for 15 minutes if 1.67V/cell is usable by your load. A normal Lead-Acid battery when fully charged has something like 2.1 V/cell. How this translates to Ah depends on the shape of the discharge curve.

If we simplify and assumed a linear drop in voltage over time (far from reality), the average voltage would be (2.1+1.67)/2 = 1.89 V. 21 W at 1.89V implies 11.14 A. 11.14A for 1/4 hour is 2.78 Ah.

-
Thanks for the info, do you have any suggestion on any method I can use to find suitable battery for my UPS? – chmod Feb 19 '14 at 10:16
@chmod: The method I use is to buy a Yuasa battery of the same chemistry, purpose, dimensions and voltage. Or buy one from the UPS maker (if it's an APC). – RedGrittyBrick Feb 19 '14 at 10:21
Note that the capacity depends on the current, for a slower discharge the capacity is approximately 4Ah – clabacchio Feb 19 '14 at 10:26

## protected by Dave Tweed♦Nov 10 '14 at 16:19

Thank you for your interest in this question. Because it has attracted low-quality or spam answers that had to be removed, posting an answer now requires 10 reputation on this site (the association bonus does not count).