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How to Calculate Elo Rating

What is Elo Rating?

The Elo rating system calculates relative skill levels in two-player games such as chess, football, or tennis. Created by Arpad Elo, it predicts match outcomes and adjusts ratings based on results.

Formula

S_A = 1 for win · 0.5 for draw · 0 for loss

Step-by-Step Guide

  1. 1Expected Score: E_A = 1 / (1 + 10^((R_B − R_A) / 400))
  2. 2New Rating: R_A = R_A + K × (S_A − E_A)
  3. 3S_A = 1 for win · 0.5 for draw · 0 for loss
  4. 4K-factor controls volatility — higher K means faster rating changes

Worked Examples

Input
Player A 1500 beats Player B 1500 at K=32
Result
A gains +16 to reach 1516, B drops to 1484
Input
Player A 1200 beats Player B 1600 at K=32
Result
A gains ~+29 upset bonus, B loses only ~3
Input
Draw between A 1800 and B 1600 at K=16
Result
A loses ~3 points, B gains ~3

Frequently Asked Questions

What is Elo Rating?

The Elo rating system calculates relative skill levels in two-player games such as chess, football, or tennis. Created by Arpad Elo, it predicts match outcomes and adjusts ratings based on results

How accurate is the Elo Rating calculator?

The calculator uses the standard published formula for elo rating. Results are accurate to the precision of the inputs you provide. For financial, medical, or legal decisions, always verify with a qualified professional.

What units does the Elo Rating calculator use?

This calculator works with inches. You can enter values in the units shown — the calculator handles all conversions internally.

What formula does the Elo Rating calculator use?

The core formula is: Expected Score: E_A = 1 / (1 + 10^((R_B − R_A) / 400)). Each step in the calculation is shown so you can verify the result manually.

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