Elo Rating Calculator
Zero-sum: what one gains, the other loses.
Work out Elo Rating. Zero-sum: what one gains, the other loses. Every rate is an input, not an assertion.
Rating change for A
+20.5
1,520 and 1,580 after · A major upset
The expected score is 1/(1 + 10^((Rb−Ra)/400)), and that 400 in the denominator is what makes a 400-point gap a 10-to-1 favourite. The scale is defined by that constant rather than derived from anything. Elo is zero-sum: whatever one player gains, the other loses. That keeps the total rating in a pool constant, which is why ratings drift over decades as players enter and leave rather than staying comparable across eras. The K-factor is the only tuning parameter and it trades responsiveness against stability. High K moves ratings quickly and makes them noisy; low K is stable and slow to reflect genuine improvement, which is why most systems vary it by experience.
How the Elo Rating Calculator works
New ratings after a result, with expected score, win probability and the size of any upset. Works for chess, tennis, esports or anything else where two rated parties meet.
Also known as: how much elo do i gain · expected score from rating difference · elo win probability · rating change after a win
Frequently asked questions
How does Elo work?
Each player has a rating, the difference predicts an expected score, and the rating moves by the K-factor times the gap between actual and expected. Beating expectations gains points; matching them gains nothing.
What does a 400-point difference mean?
A ten-to-one favourite. The 400 in the formula's denominator defines the scale — it is a chosen constant rather than something derived from data.
What is the K-factor?
How fast ratings move. High K is responsive and noisy, low K is stable and slow. Most systems use a higher K for new players and lower it as the rating settles.
Why is Elo zero-sum?
Because the winner's gain is exactly the loser's loss, keeping total rating in a pool constant. That is also why ratings drift across decades as players enter and leave.
Can Elo compare players from different eras?
Poorly. Ratings are relative to the pool at the time, so a 2500 in 1970 and a 2500 today describe standing within different populations rather than equal strength.
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