Tournament bracket calculator

What the calculator works out

A knockout tournament looks simple until you have to schedule it: 11 teams, 19 teams, 27 teams. The questions are always the same. How many games must be played, how many rounds will it take, who gets a free pass, and who plays whom? This page answers all four for any field from 2 to 4,096 teams, for single or double elimination, and lists the first-round pairings in standard seeding order so you can copy them straight into your bracket sheet.

The numbers and where they come from

Let n be the number of teams. The bracket is built for the next power of two, m = 2^r ≥ n, which also gives the number of rounds, r = ⌈log₂ n⌉. The empty places are byes: m − n of them. Real games in round 1: n − m/2. In every later round k there are m/2^k games. The total is always n − 1, because each game removes exactly one team and only the champion remains. For double elimination, every team but the champion needs two losses, so there are 2(n − 1) losses and one game per loss, plus a possible replay of the grand final: 2n − 2 or 2n − 1 games (Wikipedia, “Double-elimination tournament”).

Worked example: 11 teams

11 teams do not fill a bracket, so it is built for 16 slots: 4 rounds and 16 − 11 = 5 byes, which go to seeds 1, 2, 3, 4, 5. Round 1 has only 3 real games (8 vs 9, 7 vs 10, 6 vs 11); the winners join the five bye teams and eight teams are left, so the quarterfinals begin in round 2. The games add up to 3 + 4 + 2 + 1 = 10, one fewer than the teams. Played double elimination, the same field needs 20 games, or 21 if the grand final has to be replayed.

Common mistakes and limits

Counting byes as games. A bye is not a game, so it adds nothing to the n − 1 total. The mistake shows up when people lay out a 16-slot bracket for 11 teams and count 15 games.

Putting the byes in one corner. The standard order spreads them through the draw: with 11 teams the byes belong to seeds 1, 2, 3, 4, 5, each in its own first-round slot, because every one of those seeds is paired with an empty place. If you fill the slots left to right instead, the top seeds can end up meeting earlier than the seeding intends.

Treating the seeding as a prediction. The pairing is only as fair as the ranking behind it. It keeps seeds 1 and 2 apart until the final, but it cannot tell you the chance that the favorite wins; for the chance of one team beating another from their ratings use the Elo rating calculator.

Limits of this page. The calculator gives counts and the first-round order. It does not draw the losers bracket for double elimination or schedule courts and times, and a league's own rulebook may seed or draw byes differently.

How many games are in a single-elimination tournament?

One fewer than the number of teams. Every game sends exactly one team home, and all but the champion must go home, so 11 teams need 10 games, 8 teams need 7 and 32 teams need 31. Byes do not change this: a team that skips a game has not played one, so it does not count. Adding a third-place game makes it one more.

How many rounds does the bracket have?

The number of teams rounded up to the next power of two, then the base-2 logarithm: 11 teams fit a 16-slot bracket, which is 4 rounds. Eight teams need 3 rounds (quarterfinals, semifinals, final), 32 teams need 5, and one extra team, 33 in all, adds a whole round because the bracket jumps to 64 slots.

What is a bye, and who gets one?

A bye is a free pass into the next round. A bracket is only a clean tree when the number of teams is a power of two (2, 4, 8, 16, 32…). With any other number the bracket is built for the next power of two and the empty places become byes: 16 slots − 11 teams = 5 byes for 11 teams. The usual rule gives the byes to the best seeds, here seeds 1, 2, 3, 4, 5, which rewards the strongest teams and puts all the real games into round one. Your league may draw byes at random instead; the counts of games and rounds stay the same.

How does standard seeding pair the teams?

Best against worst, and the best seeds are kept apart. For 8 teams the first-round pairs are 1 vs 8, 4 vs 5, 2 vs 7 and 3 vs 6, listed in bracket order (1, 8, 4, 5, 2, 7, 3, 6). If the favorites always win, the pairs in the second round are 1 vs 4 and 2 vs 3, and the final is 1 vs 2, so seeds 1 and 2 cannot meet before the final. The bracket is built by doubling: each seed s in a bracket of size m is paired with m + 1 − s. The same best-against-worst rule is used for the 16 seeds of the World Snooker Championship.

How many games does double elimination need?

For n teams, 2n − 2 games at the least and 2n − 1 at the most. Each team except the champion must lose twice before it is out, which is 2(n − 1) losses, and every game produces one loss. The grand final decides whether there is one more: if the team from the losers bracket wins it, the winners-bracket champion has lost only once, so the final is played again (the “bracket reset”). Eight teams: 14 or 15 games; 11 teams: 20 or 21. It always costs about twice as many games as single elimination.

Is the best team the most likely winner of a bracket?

Only if you trust the seeding. A bracket tests every team in a short run of games, so one upset ends a team's tournament immediately, while a round-robin lets weaker teams lose several games and still finish well. If the main goal is to find the best team rather than to produce a winner quickly, use the round-robin calculator, or double elimination, which gives each team a second life. Seeding by a rating such as Elo makes the draw fairer.

Sources: Wikipedia, “Single-elimination tournament” (seeding 1 vs 8, 2 vs 7, 3 vs 6, 4 vs 5; the 16-seed pairing of the World Snooker Championship) and “Double-elimination tournament” (2n − 2 to 2n − 1 games, 14 or 15 games for eight teams). The counts n − 1 and 2(n − 1) follow from each game producing one loss. Every table on this page is checked against a simulation of brackets for 2 to 200 teams. Related: round-robin schedule calculator, Elo rating calculator, random number generator for a random draw, and permutation and combination calculator. How we check our calculators.