Not every touch on an arm is handball. The real question is whether the player used the arm in a way the law punishes, or whether the ball simply hit an arm in a situation the player could not really avoid.
For applying the Law, the upper boundary of the arm is in line with the bottom of the armpit. Contact above that boundary is treated as shoulder contact rather than handball. Once the ball contacts the hand or arm, the referee first asks whether the player deliberately moved it toward the ball. A reflexive-looking motion can still be deliberate, while a stationary arm struck unexpectedly is not automatically an offence. Distance, speed, sight of the ball, and the player's own movement help describe the action but do not replace the two legal tests.
A player commits an offence when the hand or arm makes the body unnaturally bigger and its position is not a consequence of, or justifiable by, the player's movement for that situation. Raising an arm while jumping, extending it when sliding, or using it for balance can be natural in one sequence and an unjustified barrier in another. Players take the risk of contact when placing the arm in a position that blocks substantially more space. Referees judge the full movement rather than applying a fixed rule that every arm above a particular angle is illegal.
A player cannot score directly into the opponents' goal from the hand or arm, even when the touch was accidental. It is also an offence if the scorer gains control from an accidental hand or arm touch and then scores immediately. That special outcome concerns the player who scores; an accidental touch by a teammate earlier in the attacking move is not automatically an offence unless it satisfies the ordinary deliberate or unnaturally-bigger test. VAR may check the attacking phase when such contact directly affects a goal decision.
Ordinary handball produces a direct free kick or penalty without an automatic card. A player is cautioned for handball that interferes with or stops a promising attack, subject to advantage and penalty-area exceptions. Under the current DOGSO framework, deliberate handball denying a goal or obvious opportunity is a sending-off offence wherever it occurs. A non-deliberate but punishable handball DOGSO outside the penalty area is also red; when a penalty kick is awarded for non-deliberate handball DOGSO, the defender is cautioned instead.
That question matters, but it is not the only one. Referees also ask whether the arm shape made the player bigger than the movement really needed and whether the player took a risk with that body shape.