Chess Tournament Tiebreak Calculator
Computes Buchholz, Sonneborn-Berger, and Median tiebreak scores when players finish a chess tournament on equal points. Use it to determine final standings after a Swiss or round-robin event.
Last updated: September 2026
Formula below · 2 sources (fide.com, Wikipedia) · Updated Sep 2026
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About this calculator
When players finish a tournament on equal points, tiebreak systems use the strength of opponents faced or the quality of results to separate them. The Buchholz score sums the final scores of all opponents a player faced: Buchholz = Σ opponentScore. The Sonneborn-Berger score weights each opponent's score by the player's result against them: S-B = Σ (gameResult × opponentScore), rewarding wins against strong players more than draws. The Median Buchholz variant removes both the highest and the lowest opponent score before summing (Buchholz Cut-1 removes only the lowest), reducing the effect of outlier opponents. All three methods rely on the idea that beating or drawing with high-scoring opponents is stronger evidence of performance than the same record against weak ones.
How to use
Suppose you use the Buchholz method. Your five opponents finished the tournament with scores of 4, 3.5, 3, 2.5, and 2. Enter these as '4,3.5,3,2.5,2' in the Opponent Scores field and select Buchholz. The calculator sums them: 4 + 3.5 + 3 + 2.5 + 2 = 15.0. Your Buchholz tiebreak score is 15.0. For Sonneborn-Berger with results 1, 0.5, 1, 0, 0.5 against those same opponents: S-B = (1×4) + (0.5×3.5) + (1×3) + (0×2.5) + (0.5×2) = 4 + 1.75 + 3 + 0 + 1 = 9.75. For Median Buchholz, drop the highest (4) and lowest (2) opponent scores: 3.5 + 3 + 2.5 = 9.0.
Frequently asked questions
What is the difference between Buchholz and Sonneborn-Berger tiebreak systems?
Buchholz simply adds up the total tournament scores of all opponents you faced, regardless of your individual result against each one. Sonneborn-Berger multiplies each opponent's score by your result against them (1 for a win, 0.5 for a draw, 0 for a loss), so it rewards players who scored their points against stronger opposition. Buchholz is more common in Swiss system tournaments, while Sonneborn-Berger is frequently used in round-robin events. The two systems can produce different orderings, and tournament regulations specify which applies.
When is the Median tiebreak used instead of full Buchholz?
The Median Buchholz tiebreak is used when organizers want to reduce the distorting effect of a very weak or very strong outlier opponent. It removes both the highest and the lowest opponent score before summing (the related Buchholz Cut-1 removes only the lowest), making the tiebreak more robust against the luck of pairing against an unusually weak player who later drops out. FIDE recommends it as an alternative in large open Swiss tournaments. It is particularly useful when there are bye rounds or withdrawn players whose final scores are artificially low.
How do withdrawn or forfeited games affect Buchholz tiebreak calculations?
Withdrawn players who drop out mid-tournament can deflate the Buchholz scores of everyone who played them, since their final score stays low. FIDE rules address this by replacing a withdrawn player's actual score with a virtual score (typically their score at the time of withdrawal) for tiebreak purposes. Forfeited games are typically scored as a win for the present player but the absent player receives zero, which similarly lowers Buchholz for those who played them. Tournament software usually handles these adjustments automatically, but it is worth verifying the specific regulations of each event.