Box size calculation question

I currently have a hard wires smoke alarm box, right now two 14/3 wires enter the box. I'd like to add another hard wire smoke alarm and interconnect it, so I'd be adding another 14/3 wire. Is my following calculation correct?

3 x 3 x 2 cubic inches for conducts entering the box
+ 3 x 2 cubic inches for the three conducts that are being spliced (or do I need to count 9 here?)
+ 2 cubic inches for the device (nothing for the alarm's pigtails)
= 26 cubic inches minimum

Is this correct or am I overlooking something?