Just a quick follow-up...
Roger is indeed correct about apps needing more space post-install.
For example, one of my app's .apk files is 917k (938,412 bytes)--i.e., the pre-install size.
After installing (on my Android 5.1 Nexus 5), here are the various files and the sizes (in kilobytes) of all of their various installation components:
Code:
1132 /data/data/sa.root.toolkit
928 /data/app/sa.root.toolkit-1
704 /data/dalvik-cache/arm/data@app@sa.root.toolkit-1@base.apk@classes.dex
----
2764
The Settings app reports that takes up 2.71 Mb--which is in-line with the sizes of the files above and obviously quite a bit larger than the original .apk file size (917k) [which also matches what the Play Store reports].
You should also notice that your
/data partition (which the
Storage Truth app Roger mentioned highlights) is the target for where these installation files live, so there needs to be, in this case, at least 2.71 Mb available there.
By extension, other apps will also obviously need some multiple of the .apk file's space for final installation, but that size will, of course, vary by the app and it's functionality.
Hope that helps!