Can I use a 3.7V battery for a 3.3V board?

I bought a "800mAH" 3.7v battery. Can I use it for "STM32F103C8"? This board requires 3.3 volts .If I connect a 3.7 volt battery to a 3.3 board is there a possibility of damage to the board ?
This is my battery

Yes. When freshly charged, the voltage will be significantly above 3.7V; more like 4.1V or so. That's 0.8V above the voltage you're supposed to apply to a 3.3V board. Not a good idea.

Can I reduce the voltage?

Yes, but the problem is that the voltage will decrease non-linearly as the battery is being discharged.

One way of solving this is to get a step up & down converter. Something like this: Pololu 3.3V Step-Up/Step-Down Voltage Regulator S7V8F3

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Depending on how much current the F103 will be drawing, another option might be a very low dropout 3.3V linear regulator such as the MCP1700. It will handle up to 250mA, provides regulated output with a battery voltage down to under 3.5V, and will still provide usable power below that. At 3.5V, a LIPO battery is mostly discharged anyway. So you would need the regulator and its input and output capacitors.

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What’s VBAT pin for?

Is this the only way?

Battry 3.7v
STM32F103C8 : 3.3v

For the built-in RTC of the STM32

Doesn’t look like a well designed board

It was designed for economy. They got it mostly right, there are no egregious errors. There are no electronic design problems, other than the lack of protection components in the USB interface. Sometimes the USB connector is poorly soldered, I usually dab it with some extra solder. If you want a perfect board, you get a Robodyn version for almost double the cost.

Thanks but I’ll stick with genuine arduino for now

It's apples to oranges. They're not really in a race or competition. If you want a genuine Arduino that performs as well as the STM chip that's on it, though, you will be paying more than 20x the price. If you're not familiar with it, I suggest a read of the data sheet.

ST sells some their own kits if you are looking for original OEM boards

ST Discovery Kits

Yes, and all those dev boards are supported by the official STM Arduino core.

Almost. The STM is specified 2.0-3.6V, absolute maximum 4.0V

So no problem ?

Yes, problem when the battery is fully charged, 4.2V.

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excuse me , do i have to connect 3.7v to 3.3v ?

It's answered already in post #2. Also solved in post #4.