Hi @mechanix ,
Looking at your pictures of your existing battery I believe that what you actually have is a 3.7V 1200mAH “battery” with the total minimum dimensions of 24mm x 20mm x 30mm. approx.
Are these dimensions about right for the whole unit?
If so it means that there are 3 x 3.7V 400mAH batteries, each having dimensions of 8.0mm D x 20mm W x 30 mm L (802030 figure printed on the battery) connected in parallel mode.
In parallel means that the total voltage output from the 3 batteries in the “battery” pack is the same i.e. 3.7V but the current output is cumulative i.e. 3 x 400 = 1200. Apologies if you knew this already ;-)
The usual battery sizing convention when using 6 digits is that the first 2 digits are the depth (or height if you like) with a decimal point between the digits, the next 2 digits are the width and the last 2 are the length. All measurements are in millimetres (mm).
Your proposed replacement battery is the same capacity of one “individual” battery (or cell) in the pack but it may not fit in the battery holder as it may be too wide (25mm as opposed to the 20mm there is now) or if it fits width wise and if you get three of them to make up a similar capacity battery to what you have now, it may have to be padded out to stop it moving about in the battery holder, the depth (3 x 4.0 mm = 12mm) may be to small.
If 25mm (plus a little bit due to assembly) is not too wide to fit into the holder and there are no other obstructions in the holder, you could always get 5 of the batteries that you found (6 may be pushing it) and connect them in parallel to get a 3.7V 2000 mAH battery with the overall dimensions of 20mm x 25mm x 30mm approx., which should last a lot longer than what you had with the 1200 mAH battery. Conversely it will also take longer to fully charge ;-)
Just connect the batteries’ black wires together and the red wires together and then connect the black and red wires into the BMS board (battery management system) or however it is connected.
With regard to the BMS board, it appears from your pictures that the battery has a BMS board incorporated with it. You may be able to reuse this board as the replacement batteries do not come with one and it is necessary to have a BMS which checks that the charging voltage, current and temperature of the battery is not exceeded when charging the battery. There may or may not be a temp sensor buried between the batteries. Be careful when you disassemble the old battery pack as it is still a battery and you don’t want to damage the batteries or the BMS when dismantling, unsoldering it to reclaim the BMS for reuse
Also remember to allow for the fact that the “battery” will be bigger than the combined individual battery sizes due to binding them together and connecting and insulating the wires neatly etc so make allowances for this when you go to build the battery using several batteries. Measure the interior of the battery holder to determine its’ dimensions so that you know what will fit and stay secure
If 25mm (plus a little bit due to assembly) is too wide to fit into the holder then you may be better off searching for a 802030 3.7V 400 mAH LiPO battery or the nearest equivalent in size (not bigger in any dimension unless the holder is longer in one direction) and capacity, buying 3 of them and building a “battery” to match what you have.
There are suppliers here that will supply a minimum of 1 battery with the correct voltage and dimensions that have a capacity of 400 mAH (some are 420 mAH) but double check the specification of the size because some show slightly longer or deeper sizing than the dimension numbers state which may cause problems if it is a already a tight fit in the holder.
Hopefully this has not been too long and is of some help.