Tournament Games Calculator (round robin, knockout, Swiss)

Understanding the tournament games calculator — concept and principle

An organiser needs to know how many games and rounds a format produces before booking venues. This calculator compares the three most common formats for the same number of players or teams: round robin (everyone plays everyone), single-elimination knockout, and the Swiss system.

Every line on the left is one match (120); the bracket needs only 15.

How it is calculated

Round-robin matches: n(n − 1)/2 × legs, where legs = 1 for a single round robin and 2 for home and away.
Round-robin rounds: n − 1 per leg when n is even, or n per leg when n is odd (one player sits out each round).
Knockout matches: n − 1.
Knockout rounds: ⌈log₂ n⌉, the smallest whole number of halvings that gets n down to 1.
Byes needed: 2^⌈log₂ n⌉ − n, the empty slots that fill the first round up to a power of two.
Swiss rounds for a clear winner: ⌈log₂ n⌉.

The principle

In a round robin every pair meets once, and the number of pairs among n items is the combination C(n, 2) = n(n − 1)/2. Each round can hold at most n/2 games, so an even field needs n − 1 rounds; with an odd field one player rests every round. The circle (Berger) method builds the schedule by fixing one player and rotating the rest.

A knockout is simpler still: every match eliminates exactly one player, and all but the champion must be eliminated, so there are always n − 1 matches. Because each round halves the field, the number of rounds is the base-2 logarithm rounded up. The Swiss system pairs players with similar scores; after log₂ n rounds, if nobody draws, only one player can have won every game, which is why that figure is used as the minimum.

Worked example

Inputs: n = 16 teams, single round robin (legs = 1).
Round-robin matches: 16 × 15 / 2 × 1 = 120.
16 is even, so rounds = 16 − 1 = 15 (8 games per round).
Knockout matches: 16 − 1 = 15; rounds: log₂ 16 = 4.
16 is already a power of two, so byes = 16 − 16 = 0.
Swiss rounds: ⌈log₂ 16⌉ = 4.

Each point is the calculator re-run with only “Players / teams” changed; the gold point is the default example. Change the inputs above and this chart follows your numbers.

Players / teams	Round-robin matches
4	6
8	28
12	66
16	120
20	190
24	276
32	496

How to read the result

The round robin is the fairest format but grows with the square of the field: doubling from 16 to 32 teams raises 120 matches to 496. Knockouts finish fast, but one bad day ends a run. Swiss sits in between and suits large fields with limited time. If byes are large (for example 17 players need 15 byes), consider groups followed by a knockout instead.

Common mistakes

Forgetting to double matches for home-and-away leagues.
Assuming an odd round robin needs n − 1 rounds; it needs n.
Counting a third-place play-off as part of n − 1; it is one extra match.

Keep in mind: Real Swiss events often play one or two more rounds than ⌈log₂ n⌉ because draws and ties on points are common, and tie-break rules differ by competition.

Frequently asked questions

How many games does each team play in a round robin?

n − 1 per leg, so 15 in a single round robin of 16 teams and 30 in a double one.

How do I fit 12 teams into a knockout bracket?

Use a 16-slot bracket with 4 byes, normally given to the top four seeds in the first round.

How long will a round robin take?

Rounds × time per round, if you have n/2 courts or tables to play each round at once.

Sources: FIDE Handbook, General Rules and Recommendations for Tournaments and Swiss system rules · Kenneth H. Rosen, Discrete Mathematics and Its Applications, McGraw-Hill (combinations)

Checked 8 Nov 2026. Official league / federation formulas where they exist; widely used community formulas otherwise. For fun and analysis — not betting advice.

Your numbers