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Elo Rating — Arpad Elo 1960

New = Old + K × (Actual - Expected). Expected = 1/(1+10^((Rb-Ra)/400)). K=40 new, 20 standard, 10 master. Magnus Carlsen 2882. FIDE, Chess.com.

Concept Fundamentals
E₀ + K(S − E)
Elo Update
Rating adjustment
1/(1+10^(ΔR/400))
Expected Score
Win probability
10–40 range
K-Factor
Sensitivity setting
Arpad Elo 1960
Developer
Chess → all sports
Calculate Elo ChangeUse the calculator below for arena and sports metrics

Why This Stat Matters

Why: Elo measures relative skill. 400 pts = 10:1 expected. Used in chess, esports, many games.

How: Enter your rating, opponent rating, actual score (1=win, 0.5=draw, 0=loss), K-factor. Get new rating and change.

  • Carlsen 2882 peak
  • K=40 new players, 20 standard, 10 master
  • 400 pts = 10:1 expected

📋 Quick Examples — Click to Load

1=win, 0.5=draw, 0=loss
40 new, 20 standard, 10 master
elo_analysis.shCALCULATED
New Rating
1510
Rating Change
+10
Expected Score
0.5

📊 K-Factor Impact

Upset gain by K (200-pt underdog)

📈 Expected Win %

By rating difference (400 scale)

🍩 Elo Infographic

Key facts

📊 K-Factor Comparison

Upset vs expected win gain

For educational and informational purposes only. Verify with a qualified professional.

🏅 Sports Records

♟️

Magnus Carlsen peak 2882

📊

K=40 new, 20 standard, 10 master

📐

Expected = 1/(1+10^((Rb-Ra)/400))

The Elo rating system was created by Arpad Elo in 1960 for chess. New Rating = Old + K × (Actual - Expected). Expected = 1/(1 + 10^((Rb-Ra)/400)). K-factor: 40 for new players, 20 standard, 10 for masters. Magnus Carlsen peaked at 2882. Used in FIFA, League of Legends, Overwatch. The 400 scale factor means a 400-point gap ≈ 90% expected win.

2882
Carlsen Peak
1960
Invented
400
Scale Factor
3
K-factors

Sources: FIDE, Chess.com, Arpad Elo 1960.

Key Takeaways

  • • Elo system created by Arpad Elo in 1960 for chess; now used in FIFA, gaming.
  • • Magnus Carlsen peaked at 2882, the highest Elo ever recorded.
  • • K-factor controls volatility: 40 new, 20 standard, 10 master.
  • • 400-point gap ≈ 90% expected win; 200 points ≈ 76%.

Did You Know?

♟️ Elo system created by Arpad Elo in 1960 for chess.
👑 Magnus Carlsen peaked at 2882 Elo in May 2014.
🌍 Used in FIFA rankings, League of Legends, Overwatch.
📊 K-factor controls rating volatility—higher K = bigger swings.
📐 400 scale factor: 400-pt gap = ~90% expected win.
🎮 Same formula applies across chess, esports, and sports.

How Does Elo Work?

Formula

Expected = 1/(1 + 10^((opponent - you)/400)). New Rating = Old + K × (Actual - Expected). Actual is 1 (win), 0.5 (draw), 0 (loss).

K-Factor

K=40: New players, rapid adjustment. K=20: Established. K=10: Masters, stable. FIDE uses 40 for <2400, 10 for 2400+.

Upsets

Beating a higher-rated player yields more points—your actual (1) exceeds expected. Losing to a lower-rated player costs more.

Expert Tips

Use K=20 for most calculations—it's the FIDE standard for established players.
A 400-point gap means ~90% expected—useful for quick mental estimates.
Different games use different K and scales—Chess.com and FIDE differ slightly.
Draw = 0.5 actual; some systems use fractional scores for partial wins.

K-Factor Comparison

KUse CaseUpset Gain (200 pts)
40New players~32
20Standard~16
10Master~8

Frequently Asked Questions

What is the Elo rating system?

The Elo system was created by Arpad Elo in 1960 for chess. New Rating = Old + K × (Actual - Expected). Expected = 1/(1 + 10^((Rb-Ra)/400)). It measures relative skill and predicts match outcomes. Used by FIDE, Chess.com, FIFA, and video games like League of Legends.

What is the K-factor in Elo?

K-factor controls rating volatility. K=40 for new players (rapid changes), K=20 for established players, K=10 for masters (stable). Higher K = bigger swings per game. FIDE uses K=40 for players under 2400 and K=10 for 2400+.

What is Magnus Carlsen's peak Elo?

Magnus Carlsen peaked at 2882 Elo in May 2014, the highest ever. Garry Kasparov held 2851. The 400 in the formula is a scale factor—a 400-point gap means the higher-rated player is expected to win ~90% of games.

Where is Elo used besides chess?

Elo is used in FIFA rankings, League of Legends, Overwatch, tennis, and many competitive games. The same formula applies: expected score, actual score, K-factor. Each system may use different K and scale factors.

How does the 400 scale factor work?

Expected = 1/(1 + 10^((opponent - you)/400)). A 400-point gap means ~90% expected win. 200 points = ~76%. 100 points = ~64%. The 400 makes the curve match real-world win rates in chess.

What happens when you beat a higher-rated player?

You gain more points—your actual (1) exceeds your expected (&lt;0.5). Beating a 200-point higher opponent with K=20 gains ~16 points. Losing to a much lower-rated player costs more points.

Key Statistics

2882
Carlsen Peak
1960
Invented
400
Scale Factor
3
K-factors

Official Data Sources

⚠️ Disclaimer: This calculator is for educational purposes only. Different organizations (FIDE, Chess.com, etc.) use variations of the Elo formula. Not official rating advice.

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