Math & Formula

Round Robin Tournament Formula

Instantly calculate games, rounds, and schedule size for any round robin tournament. Interactive calculator with full formula reference.

Calculator

How many teams?

6
Total games
15
n(n−1)/2
Rounds
5
n−1
Games / team
5
n−1
BYE rounds
No
Even teams — no byes
Formulas

The complete formulas

Single Round Robin
Total gamesn × (n − 1) / 2
Rounds (even n)n − 1
Rounds (odd n)n (one team has BYE per round)
Games per teamn − 1
Double Round Robin
Total gamesn × (n − 1)
Rounds (even n)2 × (n − 1)
Games per team2 × (n − 1)
Home games / teamn − 1
Knockout / Single Elimination
Total gamesn − 1 (always)
Bracket sizenext power of 2 ≥ n
Roundslog₂(bracket size)
BYE slotsbracket size − n
Quick Reference

Common team counts

TeamsSingle gamesSingle roundsDouble gamesDouble roundsKnockout rounds
333662
4631262
510520103
615530103
721742143
828756143
1045990184
126611132224
1612015240304
3249631992625
Examples

Worked through

6-team single round robin: n = 6 (even), so games = 6×5/2 = 15, rounds = 6−1 = 5. Each round has 3 simultaneous matches. No byes needed.

5-team single round robin: n = 5 (odd), so games = 5×4/2 = 10, rounds = 5 (one team has a BYE each round). Each round has 2 real matches.

8-team knockout: bracket size = 8 (already a power of 2), rounds = log₂(8) = 3, total games = 8−1 = 7. No byes.

10-team knockout: bracket size = 16 (next power of 2), rounds = log₂(16) = 4, byes = 16−10 = 6. Top 6 seeds skip round 1.

Continue
Tournament Calculator
Rounds, games, and time estimate in one tool.
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Generate a Schedule
Turn these numbers into a real printable schedule.
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Round Robin Guide
Format comparison and when to use each one.
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