I am trying to find out what size battery is used in the fossil fs4775 watch...

Fossil battery replacement sizes are usually a 2430 (CR2430), 371 (SR920SW), or 377 (SR626SW).
https://www.fossil.com/en-us/******/how-to-change-a-watch-battery

Fossil Watch Battery Replacement - Ultimate Size Guide -

batterymole.com https://batterymole.com > fossil-watch-battery-replace...
Aug 21, 2022 - The CR2430 battery is a 3v lithium battery, see the shape below. This example is made by Renata, but you can also get the produced by Duracell, ...

Tip & How-To about Watches

Changing Watch Batteries
Lots of posters ask "what is the battery in my (name of watch)" with a view to changing it yourself. This is a bad idea for many reasons. You don't have the tools or knowledge to remove a rotary screw on back, or the gasket sealant for a waterproof watch. Some fashion watches have 4 traditional screw and need professional grade jeweler screwdrivers. Also, there are about 20 batteries commonly used in watches, in various sizes and internal technology, Lithium Ion, Silver Oxide and Manganese Alkaline. If you buy them, you generally have to buy 10!

Don't sweat the details. Just take the watch to your local jeweler. They have all the batteries at hand and the tools to remove the back. It is done whilst you wait for $8 to $15!

Posted by ADMIN... on Dec 31, 2018

The vast majority of Fossil analog wristwatches take either a #377 or #379 watch battery. The #379, being slightly smaller, is somewhat more commonly found in women's watches than in men's watches, but I have seen both types used in men's and women's watches alike.
These batteries are commonly found at many drug stores, jewelry store counters at places like Walmart and Target, and even at some dollar stores. Be aware that cheap dollar store batteries are usually alkaline, not silver oxide, versions of the same size battery. Alkaline batteries may work perfectly well in many watches, but they have a somewhat different energy performance curve over time, and, in general, they won't last quite as long as a comparable silver oxide battery. In addition, for reasons I've never been able to figure out, some of the Fossil watches that I've serviced would not function with an alkaline battery--but would work fine when I put in a silver oxide battery of the same size and voltage. I have not been able to see a pattern to predict when this will and will not occur.
As a final thought, the backs of some Fossil watches are very snugly fitted to their cases. You can generally get them off without too much of a problem, but there's a good chance you may need a jeweler's press to get them to snap back on properly. I've noticed this most with round watch backs; I generally haven't needed a press to close oblong or tonneau-shaped Fossil watches (or some round watches, too). A jeweler's press spreads the pressure evenly around the edges of the watch back and watch case, preventing damaging pressure on the watch crystal, watch movement, and watch back. Clamping the watch in a regular vise to try to press on the back runs a high risk of damaging your watch, and I do not recommend trying that, no matter how frustrated you get. It's much safer (and cheaper, overall) to tip someone with a vise a couple of dollars to close up your watch for you.

Thanks for contacting Fossil.
The only way to know the battery size is to pull out the old one. It might also be in your manual. It might be on the outside of the watch.
If battery is missing, then you will have to measure the cavity and match it against a battery chart.
Best wishes.

<P>Thank you for contacting FixYa.</P><P>Unfortunately, unless it is stamped on the back of the watch, or it is in your manual, there is no way of knowing the battery that goes in any watch without the old one, or very accurate sizing of the area it goes in. You can try to contact Fossil via this link:</P><P><A href="http://www.fossil.com/en_US/shop/customer_care/static/fossil-customercare.html">http://www.fossil.com/en_US/shop/customer_care/static/fossil-customercare.html</A></P><P>Best regards.</P>

to change the battery of fossil blue watch,just open the case back and remove the old battery,look the number size on the battery and put a new battery that same number size ,after replacing battery press the case back tight to avoid water damage !good luck