Elo calculator

How many rating points is this game worth?

Enter both ratings and the result. The calculator shows your expected score, the rating change for a win, a draw and a loss, and your new rating, using FIDE's K-factor rules or a K of your choice.

Your rating

Opponent rating

Result

K-factor

Rated games played

Under 18

Rating change

+12.8

New rating about 1513. Expected score against a 1600 player: 36.0%. K = 20.

Outcome	Change	New rating
Win	+12.8	1513
Draw	+2.8	1503
Loss	-7.2	1493

Formula: expected score E = 1 / (1 + 10^{(opponent − you) / 400}); change = K × (score − E). FIDE caps the rating difference at 400 points for its tables; this calculator uses the raw formula, which differs by at most a point or two.

Working out a whole tournament or a set of games? The rating calculator adds up the change over every round and gives your performance rating.

How the Elo formula works

The system Arpad Elo designed for chess, adopted by FIDE in 1970, predicts a score from the rating gap and then moves both ratings toward what actually happened.

1. Expected score

Your expected score against an opponent depends only on the difference between your ratings:

E = 1 / (1 + 10^((opponent − you) / 400))

Equal ratings give 0.5. Every 400 points of difference multiplies the odds by ten, so a player rated 400 points higher is expected to score about 0.91: roughly ten points for every one the weaker player scores.

2. Rating change

After the game, your rating moves by the difference between what you scored (1, ½ or 0) and what you were expected to score, multiplied by K:

change = K × (score − E)

The opponent's rating moves by the same amount in the other direction when both players have the same K. That is why Elo is a zero-sum system within a pool of players.

A worked example

You are rated 1500, your opponent 1700, and K is 20. Your expected score is 0.240: the formula gives you about a 24% share of the points.

Result	Calculation	Change
Win	20 × (1 − 0.240)	+15.2
Draw	20 × (0.5 − 0.240)	+5.2
Loss	20 × (0 − 0.240)	−4.8

A win is worth three times what a loss costs, because the loss was the expected result. That asymmetry is the whole point of Elo: beating stronger players moves you up quickly, losing to them costs little.

Expected score by rating gap

For the higher-rated player, with the change at K = 20.

Gap	Expected	Win	Draw	Loss
0	0.50	+10.0	+0.0	−10.0
50	0.57	+8.6	−1.4	−11.4
100	0.64	+7.2	−2.8	−12.8
150	0.70	+5.9	−4.1	−14.1
200	0.76	+4.8	−5.2	−15.2
250	0.81	+3.8	−6.2	−16.2
300	0.85	+3.0	−7.0	−17.0
350	0.88	+2.4	−7.6	−17.6
400	0.91	+1.8	−8.2	−18.2

FIDE K-factors

K decides how fast a rating reacts. FIDE uses three values.

40New players, until they have completed 30 rated games; and players under 18 whose rating is below 2300.
20Everyone else rated below 2400.
10Players who have reached 2400 at any point. The lower K stays even if the rating later drops.

A higher K lets a new or improving player reach their true level quickly; a lower K keeps established ratings stable. Choose “FIDE rules (auto)” in the calculator and it applies these rules from your rating, games played and age.

Elo calculator questions

Why is my Chess.com or Lichess rating change different?

Neither site uses plain Elo. Chess.com uses the Glicko system and Lichess uses Glicko-2. Both track how certain your rating is: a player with few recent games has a large rating deviation and moves many points per game, while an active player with a settled rating moves fewer. The expected-score idea is the same, so this calculator gives the right direction and a reasonable size, but not the exact number those sites will show.

Which K-factor should I use?

For FIDE-rated games, choose FIDE rules and enter how many rated games you have played and whether you are under 18; the calculator picks 40, 20 or 10 for you. National federations, leagues and clubs set their own rules, so pick Custom and enter their K if you know it.

Why do I gain so little for beating a lower-rated player?

Because the formula already expected you to win most of the time. Against an opponent 200 points below you, your expected score is about 0.76, so a win earns only the remaining 0.24 times K, and a loss costs 0.76 times K. Rating points move most when the result is a surprise.

Is a draw against a stronger player good for my rating?

Yes. A draw is a score of 0.5. Whenever your expected score is below 0.5, which it is against anyone rated higher than you, a draw gains points. Against a player rated 200 points higher, a draw at K = 20 is worth about five points.

Does the calculator apply FIDE's 400-point rule?

No. FIDE counts any rating difference above 400 as if it were exactly 400. The calculator uses the raw formula, so for very lopsided pairings its figure differs from FIDE's by a point or two at K = 20. For gaps of 400 points or less the two agree.