I have a background for my app in resolutions 720x1280 pixels, 1080x1920 pixels and 1440x2560 pixels.
In which folders (mdpi, hdpi, xhdpi and xxhdpi) should I put each background?
Please read the Android Documentation regarding screen sizes.
From a base image size, there is a 3:4:6:8:12:16 scaling ratio in drawable size by DPI.
LDPI - 0.75x
MDPI - Original size // means 1.0x here
HDPI - 1.5x
XHDPI - 2.0x
XXHDPI - 3x
XXXHDPI - 4.0x
For example, 100x100px image on a MDPI will be the same size of a 200x200px on a XHDPI screen.
DP size of any device is (actual resolution / density conversion factor).
Density conversion factor for density buckets are as follows:
ldpi: 0.75
mdpi: 1.0 (base density)
hdpi: 1.5
xhdpi: 2.0
xxhdpi: 3.0
xxxhdpi: 4.0
Examples of resolution/density conversion to DP:
ldpi device of 240 X 320 px will be of 320 X 426.66 DP. 240 / 0.75 = 320 dp 320 / 0.75 = 426.66 dp
xxhdpi device of 1080 x 1920 pixels (Samsung S4, S5) will be of 360 X 640 dp. 1080 / 3 = 360 dp 1920 / 3 = 640 dp
This image show more:
For more details about DIP read here.
in order to know the phone resolution simply create a image with label mdpi, hdpi, xhdpi and xxhdpi. put these images in respective folder like mdpi, hdpi, xhdpi and xxhdpi. create a image view in layout and load this image. the phone will load the respective image from a specific folder. by this you will get the phone resolution or *dpi it is using.
Your inputs lack one important information of device dimension. Suppose now popular phone is 6 inch(the diagonal of the display), you will have following results
DPI: Dots per inch - number of dots(pixels) per segment(line) of 1 inch. DPI=Diagonal/Device size
Scaling Ratio= Real DPI/160. 160 is basic density (MHDPI)
DP: (Density-independent Pixel)=1/160 inch, think of it as a measurement unit