Elo win probability calculator
Find the expected score for any rating gap, or the gap you need for a target probability. In Elo the expected score counts a draw as half a win, so 0.64 means "64% of the points", not "wins 64% of games".
Reverse: what gap gives a target probability?
The formula
P(A) = 1 / (1 + 10^(−D / s)) D = R_A − R_B, s = 400 (chess) or 600 (FIFA)
D = −s × log10(1/P − 1) (the reverse)
US Chess publishes this logistic curve with s = 400 as its "standard winning expectancy".[1] FIFA's men's ranking uses the same shape with s = 600, which makes each point of rating gap count for less.[3] FIDE uses a lookup table instead of the formula, and caps gaps at 400 for players rated below 2650.[2]
| Gap | Logistic, 400 | FIDE table | FIFA, 600 |
|---|---|---|---|
| 50 | 57.1% | 57% | 54.8% |
| 100 | 64.0% | 64% | 59.5% |
| 200 | 76.0% | 76% | 68.3% |
| 300 | 84.9% | 85% | 76.0% |
| 400 | 90.9% | 92% | 82.3% |
| 500 | 94.7% | 92% | 87.2% |
| 600 | 96.9% | 92% | 90.9% |
FIDE column for a player rated under 2650, so gaps above 400 count as 400. See the full table from 0 to 800.
Reading the result
- Expected score is not a prediction of one game. It's the average result over many games. A 0.76 favourite still loses or draws some games.
- Draws matter. In a game with many draws, like top-level chess, a 0.64 favourite might win only a minority of games and draw most of the rest. Elo doesn't model the draw rate separately.
- Ratings from different pools don't mix. A gap only means something when both ratings come from the same system. See Chess.com vs Lichess vs FIDE.
To update ratings after a result, use the Elo calculator.
Sources
- Glickman, M. E. & Doan, T. The US Chess Rating System (specification dated 2026-04-06), sections 3 and 4.2 — US Chess Federation
- FIDE Rating Regulations, effective 1 March 2024 (with the 400-point rule as amended from 1 October 2025), sections 7–8 — FIDE Handbook
- Revision of the FIFA/Coca-Cola World Ranking (SUM method) — FIFA