Instrument № 1
Elo Change Calculator
The FIDE formula, game by game. Enter your rating and K-factor, then one opponent or a whole mini-tournament - every ΔR is computed with the official Table 8.1.2 expectation.
Rating change
- K used
- 20
- Expected score
- 0.50= 50%
- Σ (S − E)
- +0.50
| Game | Opponent | Diff D | E | S | ΔR |
|---|
The arithmetic
How your rating change is computed.
Two numbers decide every game: your expected score E and the coefficient K. The FIDE system reads E from its official table - rating difference D = your rating minus your opponent's, capped at 400 for under-2650 players - and then pays ΔR = K × (S − E) for the game[F1]. Win as the underdog and S − E is large and positive; lose as the favourite and it cuts the same deep.
Worked examples - verify them above
The second example shows why the table matters: the exact logistic curve would give E ≈ 0.909 and ΔR ≈ +0.9, but FIDE's published table reads 0.92 at D = 400 - switch the method toggle to see both.
Choosing your K-factor
Set K to Auto and answer the three questions, or pick it yourself: K = 40 covers your first 30 rated games and juniors under 18 (below 2300); K = 20 covers established players under 2400; K = 10 belongs to anyone who has published 2400 - permanently[F1]. If K × games-in-period would exceed 700, FIDE lowers K for that period.
Multi-game events
FIDE settles ratings once per period: it sums (S − E) across all your games and multiplies by your K for that period, rounding the total to the nearest whole point, 0.5 away from zero[F1]. The table above follows that official style. Our sequential projection (shown when it differs) instead re-rates you after every game - useful for seeing how a hot streak compounds.
Want the expectation without the delta? Expected score calculator · turning a cross-table into a TPR? Performance rating calculator · planning the climb? Rating goal planner · still unsure about K? What K-factor am I?