Rule of the square

The rule of the square quickly shows whether the defending king can catch a pawn running alone toward promotion, when it reaches the last rank and becomes another piece. First imagine the square of the pawn, whose side length reflects the number of pawn moves remaining.

If the defending king is already inside the square, it can normally catch the pawn. If it is the king's turn and the king can enter the square immediately, it also arrives in time. If the pawn's side moves first, the pawn advances and the square shrinks before the king approaches. The side to move can therefore decide the race.

The rule assumes a simple contest: an unsupported pawn, a clear path, and no checks or obstacles that alter the timing. An attacking king may block the defender's route, and other pieces can change the result. Treat the rule as a fast first test, not a complete evaluation of every endgame.