Powder Boxes will detonate if anything hits them, such as a thrown object. They will even explode from otherwise non-interacting particles, such as spattering blood drops or rock chunks from destroyed ground blocks. Therefore, you should be mindful when fighting enemies or mining with the mattock near a Powder Box.
They can be walked on top of safely, and can even be pushed like push blocks, but will explode if they fall off a ledge and land more than one block down. They will explode immediately if they hit a monster (like a Bat) in midair. Pushing a powder box through a skeleton or a pot on the floor triggers its explosion. Breaking treasures through pushing it with a powder box against a wall also triggers its explosion.[Needs Research]
Nearby explosions will also set off Powder Boxes, even if they are out of the blast radius, because they will get hit from rock chunks that spew out of the explosion. This often causes chain reactions when several Powder Boxes spawn in close proximity. Powder boxes happen to catch contact from rock chunks from diagonal directions, thus exploding even if protected by blocks in orthogonal direction.
Powder Boxes cannot be rendered safe, so the best strategy for dealing with them is to set them off from a distance.
An object may be thrown at them from afar, but be mindful that the explosion may propel it back at you. If possible, use an item that shatters on impact, such as a pot or skull, or an item that causes no damage (such as a broken arrow shaft or a critter). If you use a rock or arrow, it is liable to bounce back at you and inflict damage.
If no safe and free method of triggering it is available, a Bomb may be placed nearby, using the fuse time to run away from the explosion. Do not place the Bomb directly against the Powder Box or it will explode immediately like when hit by any other object.
If the Powder Box lies on a ledge above a tall shaft, it is safe to push the box off the edge so that it explodes at the bottom of the pit.