How many ways can a chessboard be set?

An exact upper bound on the number of chess positions, built from four counting steps. Hover over, tap or click any part of the formula to see what it counts on the board.

The formula

Explore one material

Material on the board

Design a different game

What if chess had more piece types, more copies of each, or a different board? Change anything below and the whole page, including the formula, the board and the totals, recalculates for your game.

LetterPiecePer sidePawns promote to itRemove

Each side always has one king. Pawns can stand on any square except the first and last ranks.

Choosing which pieces are left

Before any squares are chosen, the bound needs to know which pieces can still be on the board. Ignore kings, pawns and promotions for a moment. Each column below is one kind of piece in the current game, for both colours. Click a cell to choose how many of that piece remain; click the top kept cell again to remove one.