I made an app that includes a battle calculator. “Axis & Allies Utility” on iOS. “Utility for Axis & Allies Game” on Android.

Although in a real game i prefer to do the calculations in my head. Similar to what the first reply said, add up the total numbers for attack and defense, and divide by 6 to get an average amount of hits.

ex: attackers 2 tanks (6) + 1 inf (1) + 6 bombers (24) = 31 avg. 31/6 = 5 + 1/6 … round to 5

defenders 14 inf (28) = 28 avg. 28/6 = 4 + 2/3 … round to 5

now you can continue by removing the hits. At this point though it may help to get a pencil and paper.

After removing hits (just removing lowest combat value)

4 bombers (16) = 2 + 4/6 ~ 3

9 inf (18) = 3 hits

… and again

1 bombers (4) = ~ 1 hit

6 inf (12) = 2 hits but only need 1.

So the defenders win pretty easily with 5 infantry remaining. I used this example to show that even though the attackers and defenders had similar combat values at first, (attackers even had a bit more), the defender was able to take smaller hits, and win the battle pretty easily.