Round-robin schedule calculator

What the calculator works out

A round-robin is the simplest fair format: everyone plays everyone. The hard part is practical. A coach or league organizer needs to know how many games to book, how many weeks that fills, and who plays whom in week 3. This page gives the totals first, then a complete schedule built with the circle method, with a rest round for the odd team out and home and away games shared out as evenly as possible. It handles 2 to 40 teams, once or twice around.

The numbers

Let n be the number of teams. The number of games is the number of pairs, n(n − 1)/2, or n(n − 1) if each pair meets twice. Each team plays n − 1 games (twice that in a double round-robin). If n is even, there are n − 1 rounds of n/2 games, with all teams playing every round; if n is odd, there are n rounds of (n − 1)/2 games, and one team rests in each (Wikipedia, “Round-robin tournament”).

Worked example: six teams

Six teams play 6 × 5 ÷ 2 = 15 games in 5 rounds of 3 games. The calculator's schedule, home team first:

• Round 1: 6 v 1, 2 v 5, 3 v 4
• Round 2: 1 v 2, 5 v 3, 4 v 6
• Round 3: 3 v 1, 6 v 2, 4 v 5
• Round 4: 1 v 4, 2 v 3, 5 v 6
• Round 5: 5 v 1, 4 v 2, 6 v 3

Check it: team 1 meets 2, 3, 4, 5 and 6 once each, and no team appears twice in a round. Every team has 2 or 3 home games out of 5; the schedule has 4 breaks, which is the minimum n − 2 = 4 for six teams. Add a seventh team and the same method gives 7 rounds of 3 games with one team resting each round (21 games in all).

Common mistakes and limits

Mixing up games and rounds. 8 teams play 28 games but only 7 rounds, because 4 games run at once. Book fields or courts for the games per round, not the total.

Forgetting the odd team. With an odd field the number of rounds equals the number of teams, not one fewer. A season planned as n − 1 weeks for 9 teams would leave every team one game short.

Expecting no breaks. A schedule in which each team alternates home and away every round is impossible for an even number of teams: de Werra's bound says at least n − 2 breaks, and this calculator reaches it. Some pairs of consecutive home games are unavoidable.

Limits. The schedule does not know about venues, travel, holidays, rest days or teams that must not play early. If a team cannot play in a round, the pairing has to be moved by hand, as Wikipedia notes. The circle method is one of several valid schedules; for asynchronous play with rest between games a different order is better for an odd number of teams.

How many games are in a round-robin tournament?

Every team plays every other team once, so the number of games is the number of pairs: n × (n − 1) ÷ 2. Six teams play 15 games, 10 teams play 45, and 14 teams play 91. If each pair meets twice (home and away), double it: 10 teams then play 90 games, and each team plays 18.

How many rounds does a round-robin need?

With an even number of teams, n − 1 rounds, and every team plays in every round: 14 teams need 13 rounds of 7 games each. With an odd number of teams there are n rounds, and in each round one team has no opponent and rests; seven teams need 7 rounds of 3 games. That is why an odd field takes one more round than the even field just above it, and why a league with 9 teams is scheduled the same way as one with 10, with one team resting each round. A double round-robin doubles the number of rounds.

How does the circle method build the schedule?

Write the teams in two rows, top and bottom, and pair each team with the one facing it. Keep team 1 fixed, rotate all the others one place around the circle, and pair again; repeat until the pairings start to repeat. With n teams (n even) that takes n − 1 rounds and every possible pair appears exactly once. For an odd n you add a dummy team, and whoever is paired with the dummy has the round off. The calculator uses an equivalent form of the same rotation: in round r the teams i and j meet when i + j leaves the remainder r after division by n − 1.

How are home and away games balanced?

Home and away follow from the table position: the fixed team has to alternate between rounds, and the others are assigned so that no team has more than one extra home or away game. In this schedule the home and away counts of every team differ by at most one (3 and 3 for each of seven teams; 4 teams with 4 home games and 4 with 3 among eight). The unavoidable irregularity is the “break”: two home or two away games in a row. De Werra showed that with an even number of teams any schedule has at least n − 2 breaks, and this one has exactly 6 for 8 teams. With an odd number of teams the schedule has none.

What is a Berger table?

A printed round-robin pairing chart for chess tournaments, named after the Austrian master Johann Berger, who published tables of this kind in the 1890s and credited Richard Schurig as the inventor. In a Berger table one player stays fixed while the others rotate, the same idea as the circle method (Wikipedia, “Round-robin tournament”). For a real chess event, follow the table in your federation's rules for the numbering, since the colors and the player order are part of the official table.

Is a round-robin better than a knockout bracket?

It is fairer and much longer. A round-robin gives every team the same number of games against the same opponents, so the standings say more about strength than a single lucky day, but 8 teams already need 28 games where a single-elimination bracket needs 7, and 16 teams need 120 against 15. Many leagues therefore play a round-robin to rank the teams and a short knockout between the best of them. The tournament bracket calculator counts the knockout side.

Sources: Wikipedia, “Round-robin tournament” (n(n − 1)/2 games, n − 1 rounds for an even number of teams and n for an odd number, the circle method with a dummy team for byes, Berger tables with their references to Schurig 1886 and Berger 1893); for the break bound, the survey “Minimizing breaks by minimizing odd cycle transversals” (arXiv 2411.15463), which attributes the n − 2 lower bound for an even number of teams to D. de Werra (1981). The schedule on this page is checked for 2 to 40 teams: each pair meets exactly once, nobody plays twice in a round, and home and away games differ by at most one. Related: tournament bracket calculator, Elo rating calculator, permutation and combination calculator (n choose 2 pairs) and random number generator for the draw. How we check our calculators.