Elo Rating Change Calculator

Expected score and the new rating after one association football match, from two Elo ratings, a K value and the result. K and the scale divisor are inputs, because no implementation’s values are universal.

Last updated 12 Oct 2026

New Elo rating after one match

Ratings → expected score

This team’s rating before the matchThe rating you are updating. Elo ratings have no absolute meaning: only the difference between two of them does anything, which is why a rating from one published system cannot be dropped into another.

The opponent’s rating before the matchFrom the same rating list as the figure above. Mixing lists is the commonest way to get a confident wrong answer here.

K, the weight given to this matchHow much one result is allowed to move a rating. There is no universal value: FIDE publishes 25, 15 and 10 by a player’s experience and rating, and FIFA’s world-ranking method puts an importance coefficient of 5 to 60 in the same place. The table below lists FIFA’s whole set.

The actual result for this teamElo’s actual score S. A draw is half a win — the assumption that makes the arithmetic work, and one of the system’s known simplifications, since it treats every win as the same win whatever the scoreline.

Scale divisorA choice of scale rather than a law. At 400, a 400-point lead gives ten to one, which is what the 400 is for. FIFA’s published method divides by 600, so there it takes a 600-point gap. The two scales are not interchangeable.

1,814.40rating after the matchExample

A team rated 1800 beats a team rated 1700, with K = 40 on the 400-point scale

Formula

Expected score: E = 1 ÷ (1 + 10^{(R_B − R_A) ÷ D})
New rating: R′ = R + K × (S − E)
D = 400 on Elo’s own scale; D = 600 in FIFA’s published world-ranking method; S = 1 for a win, 0.5 for a draw, 0 for a defeat

E, the expected score: the long-run average score the rating difference implies, not a win probability: 0.64 is consistent with many mixtures of wins and draws. Glickman and Jones state the same formula with D = 400 and give a 0.91 winning expectancy at a 400-point difference, which this page reproduces
D, the scale divisor: the gap at which the expected score ratio reaches ten to one. Elo chose 400; FIFA’s published method uses 600, so a 400-point lead is 0.9091 on one scale and 0.8227 on the other. Both are internally consistent and the two are not interchangeable
K: the weight on one result, and an input because nobody’s value is universal. FIDE publishes 25, 15 and 10 by player experience and rating. FIFA publishes an importance coefficient I from 5 to 60 by match type, in the same position in the formula. A large K makes a rating responsive and noisy; a small one makes it stable and slow
S: the actual score: 1, 0.5 or 0. This is where the plain method throws information away, because a 5-0 win and a 1-0 win are both S = 1. Football implementations commonly add a goal-difference index and a home-advantage term to recover some of it, and this page implements neither — it would be reproducing somebody else’s constants

Worked example

A team rated 1800 beats a team rated 1700, with K = 40 on the 400-point scale
E = 1 ÷ (1 + 10^{(1700 − 1800) ÷ 400}) = 1 ÷ (1 + 0.5623) = 0.6401, so the opponent's expected score is 0.3599 and the two sum to exactly 1
S − E = 1 − 0.6401 = 0.3599
R′ = 1800 + 40 × 0.3599 = 1,814.40, a gain of 14.40 points, and the opponent loses exactly 14.40 because the update is zero-sum at a common K
A draw gives 1,794.40 and a defeat 1,774.40 — the favourite loses rating for drawing, which is the system working rather than a quirk
Switch the divisor to FIFA's 600 and E falls to 0.5948, so the same win is worth more: a flatter scale treats a 100-point lead as less decisive

Expected score against the rating lead, on both published scales

Every figure is this calculator’s own arithmetic. Read the +400 row: 0.9091 is exactly ten to one, and that is what the number 400 is for — the gap chosen to make the ratio ten to one, with nothing about football forcing it. On FIFA’s published 600 divisor the same lead is worth 0.8227 and it takes 600 points to reach ten to one. Neither is wrong; they are different scales.
Rating lead	Expected score at D = 400	Expected score at D = 600	Expected score ratio at D = 400
0	0.5000	0.5000	1.00 to 1
+50	0.5715	0.5478	1.33 to 1
+100	0.6401	0.5948	1.78 to 1
+200	0.7597	0.6830	3.16 to 1
+300	0.8490	0.7597	5.62 to 1
+400	0.9091	0.8227	10.00 to 1
+600	0.9693	0.9091	31.62 to 1
+800	0.9901	0.9556	100.00 to 1

FIFA’s own importance coefficients, which sit where K sits

From FIFA’s own “Revision of the FIFA / Coca-Cola World Ranking”, which states the method as P = P(before) + I × (W − We) with We = 1 ÷ (10^(−dr/600) + 1). FIFA calls the weight an importance coefficient and sets it by the match rather than by the team, which is why a World Cup quarter-final moves a ranking twelve times as far as a friendly in a quiet week. These values belong to FIFA’s men’s world ranking and to nothing else: K is an input on this page because there is no universal value, and a rating computed with one set of coefficients is not comparable with one computed with another.
Match type	I
Friendly played outside an International Match Calendar window	5
Friendly played during an International Match Calendar window	10
Nations League group-phase match	15
Nations League play-off and final match	25
Qualifier for a confederation final competition or the FIFA World Cup	25
Confederation final competition match up to the quarter-finals	35
Confederation final competition match from the quarter-finals, and all FIFA Confederations Cup matches	40
FIFA World Cup final competition match up to the quarter-finals	50
FIFA World Cup final competition match from the quarter-finals	60

The method is published; the parameters belong to whoever chose them

The sport is association football — soccer. Elo is used in many sports and in chess, where it began, but the parameter values quoted on this page are the ones published for association football, and they do not carry across to another code. Elo is the one rating system on this site that a page can legitimately implement, and the reason is that the method is published rather than sold. Arpad Elo set out the theory, FIDE publishes the rating-change formula and its rating-difference-to-probability table openly in its Handbook, Glickman and Jones restate the same two equations in the statistical literature, and FIFA published its own Elo-based world-ranking method as a free document with every coefficient in it. Nothing read while writing this page suggested a licence, a fee or a permission requirement for the method itself. That is a weaker claim than “it is in the public domain” and it is the claim the evidence supports.

The arithmetic has two halves: the expected score turns a rating difference into a long-run average score, and the update moves the rating by K times the gap between what happened and what was expected. Three properties fall straight out of the formula and are worth checking against any Elo calculator: equal ratings give exactly 0.5; the two expected scores add to 1; and the expected score is strictly between 0 and 1 at every difference, so no gap makes a result certain. The fourth defines the scale — at the 400 divisor a 400-point lead gives 0.9091, exactly ten to one. Glickman and Jones put that at 0.91, and a 1500 against a 1700 at about 0.24 for the weaker player; this page reproduces both.

Where implementations part company is the parameters, and football is where they part company most. FIFA’s own men’s world ranking moved to an Elo-based method and divides the rating difference by 600 rather than 400, which flattens the scale: on FIFA’s arithmetic a 400-point lead is worth 0.8227 and it takes 600 points to reach ten to one. FIFA also replaces K with an importance coefficient set by the match, from 5 for a friendly outside an International Match Calendar window to 60 for a World Cup match from the quarter-finals onward. FIDE, for the same formula, publishes 25, 15 and 10 by a player’s experience and rating. None of those is football’s value, and a rating produced with one set of constants cannot be read against a rating produced with another.

Two things this page deliberately does not do. It does not add a goal-difference term or a home-advantage term, both of which some published football Elo systems use, because reproducing another system’s constants would present somebody else’s parameterisation as the general method — and one such system’s own description could not be read while this page was written, so it is not reproduced here rather than guessed at. The update is zero-sum at a common K, which FIFA’s method does not always hold because its coefficient is set by the match. And it does not convert anything into a price. This page does not price anything, convert a bookmaker’s odds, or estimate a stake. It does arithmetic on figures a competition or a statistics provider publishes. Every figure on this page is printed with the body that publishes it and the season or edition it belongs to, because a football number is usually a regulation rather than a fact, and regulations are revised. Check the playing conditions or competition regulations for the competition in front of you before relying on a default.

Frequently asked questions

What is the Elo expected score formula?

E = 1 ÷ (1 + 10 to the power of (opponent’s rating − your rating) ÷ 400). Glickman and Jones state it in exactly that form. At equal ratings it is 0.5; at a 400-point lead it is 0.9091, a ratio of ten to one, which is what the 400 in the formula is chosen to produce.

What K value should I use for football?

There is no single answer, which is why K is an input here. FIFA’s own world-ranking method uses an importance coefficient in K’s place, running from 5 for a friendly outside an International Match Calendar window to 60 for a World Cup match from the quarter-finals. FIDE’s published rating regulations use 25, 15 and 10. Pick the value the system you are reproducing uses, and say which one you used.

Why does FIFA divide by 600 instead of 400?

Because the divisor is a choice of scale, not a law. FIFA’s published method states the expected result as 1 ÷ (10 to the power of (−dr/600) + 1). The effect is a flatter scale: a 400-point lead is worth 0.8227 rather than 0.9091, and it takes a 600-point gap to reach ten to one. A FIFA ranking point and a 400-scale Elo point are therefore not the same unit.

Does Elo account for the margin of victory?

Not in the plain method. S is 1, 0.5 or 0, so a 5-0 win and a 1-0 win move a rating identically. Some published football implementations add a goal-difference index and a home-advantage term for that reason. This page implements neither, because that would mean reproducing another system’s constants and presenting them as the general method.

Is the expected score a betting probability?

No. It is the long-run average score a rating difference implies, computed from two ratings and nothing else — not a price, not derived from one, and not converted into one anywhere on this site. It also cannot be read as a win probability on its own, because an expected score of 0.64 is consistent with many different mixtures of wins and draws.

Related calculators

References

FIFA. Revision of the FIFA / Coca-Cola World Ranking. Zurich: FIFA. Points formula P = P_before + I × (W − W_e); expected result W_e = 1 / (10^(−dr/600) + 1); importance coefficients I of 5, 10, 15, 25, 35, 40, 50 and 60 by match type.
FIDE. Rating-system regulations, FIDE Handbook (articles 10.1 onward). Rating change DR = K(W − W_e), with FIDE’s published table converting a rating difference into a scoring probability, and development coefficients K of 25, 15 and 10.
Glickman ME, Jones AC. Rating the Chess Rating System. Boston University and Reed College; manuscript at glicko.net/research/chance.pdf. States the Elo expected score as E = 1 / (1 + 10^{−(R_A−R_B)/400}) and the update as r_post = r_pre + K(S − S_exp), and gives a 0.91 winning expectancy at a 400-point difference. The journal of record was not shown on the copy read, so none is claimed here.