# Elo Rating Calculator

> Calculate rating change after a match using the standard Elo formula for chess or competitive games

**Category:** Utility
**Keywords:** calculator, tool
**URL:** https://complete.tools/elo-rating-calculator

## How the Elo Formula Works

The Elo system uses two key formulas to compute rating changes after a match.

**Expected Score:**
```
E_A = 1 / (1 + 10^((R_B - R_A) / 400))
```

This gives the probability (between 0 and 1) that Player A will score against Player B. If both players have equal ratings, the expected score is 0.5 for each.

**New Rating:**
```
R'_A = R_A + K * (S_A - E_A)
```

Where:
- **R_A** and **R_B** are the current ratings of Players A and B
- **E_A** is the expected score for Player A
- **S_A** is the actual score: 1 for a win, 0.5 for a draw, 0 for a loss
- **K** is the K-factor, which controls how much ratings change per game

The constant 400 in the expected score formula means that a player rated 400 points above their opponent is expected to score about 91% of the time.

## Understanding the K-Factor

The K-factor determines the maximum number of rating points a player can gain or lose from a single game. Choosing the right K-factor depends on the context:

- **K = 10**: Used for established, high-rated players. FIDE applies this to players rated above 2400. Rating changes are small and stable.
- **K = 20**: The standard K-factor used by FIDE for most rated players. It balances responsiveness with stability.
- **K = 32**: Originally used by the USCF for all players. Common in online platforms. Good for newer players whose true skill level is still being determined.
- **K = 40**: Used by FIDE for players who have not yet completed 30 rated games. Allows ratings to converge quickly to a player's actual strength.

A higher K-factor makes ratings more volatile and responsive to recent results. A lower K-factor produces more stable ratings that change gradually over time.

## Common Elo Rating Scales

Rating ranges vary by organization, but here are some general benchmarks:

**Chess (FIDE):**
- Below 1200: Beginner
- 1200-1400: Casual club player
- 1400-1600: Intermediate club player
- 1600-1800: Strong club player
- 1800-2000: Expert / Candidate Master
- 2000-2200: National Master level
- 2200-2400: FIDE Master / International Master
- 2400-2600: Strong Grandmaster
- 2600-2800: Super Grandmaster
- 2800+: World Championship contender

**Online Gaming:** Many platforms use similar systems with different scales. Chess.com and Lichess both use Elo-derived systems, though their absolute numbers differ due to different rating pools and K-factors.

## How to Use This Calculator

1. Enter Player A's current rating in the first field
2. Enter Player B's current rating in the second field
3. Select the appropriate K-factor for your context
4. Choose the match result using the segmented control
5. View the updated ratings, expected scores, and point changes instantly

## FAQs

**
**Q:** What starting rating should a new player use?**


**A:** Most organizations assign new players a default rating of 1500 or 1200. FIDE assigns an initial rating based on early tournament performance. For casual use, 1500 is a common starting point.

**
**Q:** Can Elo ratings go below zero?**


**A:** Mathematically the formula allows it, but in practice most systems set a floor (often 100 or 0). Extremely low ratings are rare because lower-rated players lose fewer points when they lose.

**
**Q:** Why do some platforms show different ratings for the same player?**


**A:** Different platforms use different K-factors, starting ratings, and rating pools. A player rated 1800 on one site might be rated 1500 on another. The relative rankings within a single system are what matter.

**
**Q:** Is the Elo system fair for draws?**


**A:** Yes. A draw is treated as a score of 0.5. If a lower-rated player draws against a higher-rated player, the lower-rated player gains points and the higher-rated player loses points, reflecting the upset.

**
**Q:** How many games does it take for an Elo rating to stabilize?**


**A:** With a high K-factor (32-40), ratings converge within 20-30 games. With a standard K-factor (20), it typically takes 50 or more games for the rating to reliably reflect a player's true strength.

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*Generated from [complete.tools/elo-rating-calculator](https://complete.tools/elo-rating-calculator)*