Elo Calculator: Rating Change and Win Probability

Elo rating calculation: expected score and the K-factor

A player’s expected score is 1 / (1 + 10^((opponent rating − player rating) / 400)), and the rating change is K × (result − expected score). At 1500 against 1600 the expected score is 36.0%; with K = 20, the default, a win gains 13 points and a loss costs 7.

Formula used by the tool

Expected score: E = 1 / (1 + 10^((Rb − Ra) / 400)). Change: K × (S − E) with S = 1 for a win, 0.5 for a draw and 0 for a loss; the tool rounds each change to a whole number. The percentage shown is the expected score, which counts a draw as half a point, so it is not a strict probability of winning.

Example

A 1500 player against a 1600 opponent: E = 1 / (1 + 10^0.25) = 0.3599. With K = 20 (the default): win +13, draw +3, loss −7. With K = 32: +20, +4 and −12. Against a 2000 player, E falls to 5.3% and a win earns +19 with K = 20 (+30 with K = 32).

K-factor: tool versus FIDE

The tool starts at K = 20 and offers the three values of the FIDE rating regulations (art. 8.3.3): K = 40 for a player new to the list until they have completed at least 30 games, and for juniors until the end of the year of their 18th birthday while their rating stays under 2300; K = 20 while the rating stays under 2400; K = 10 once a published rating has reached 2400 and remains at that level. K = 32 is a generic value that FIDE does not use. A field also accepts any K from 1 to 100.

FIDE rules the tool does not apply: if K × the number of games in the rating period exceeds 700, K becomes the largest whole number such that K × n does not exceed 700; a gap of more than 400 points counts as 400 for players rated below 2650 (art. 8.3.1); FIDE rounds the total change for the period, 0.5 being rounded away from zero (art. 8.3.4), whereas the tool rounds each game; a player who drops below 1400 is shown as unrated on the next list (art. 7.2.1).

Tiers

The tiers shown (bronze to International Master) are the tool’s own labels and match no specific video game rank, whose MMR often uses other formulas. The top two use FIDE title rating thresholds: 2300 for the FIDE Master title, 2400 for International Master. The Grandmaster title requires 2500, and the International Master and Grandmaster titles also require norms.

Sources and dates: FIDE Rating Regulations applied from 1 March 2024, art. 7.2.1 (1400 floor), 8.3.1 (400-point rule, version of 1 October 2025), 8.3.3 (K-factor) and 8.3.4 (rounding); FIDE Title Regulations applied from 1 January 2024, art. 1.3.1 and 1.5.3 (checked 28/10/2026).

Frequently Asked Questions

How many Elo points do I gain by beating a higher-rated player?

The gain is K × (1 − expected score). At 1500 against 1600, a win earns 13 points with K = 20 and 20 with K = 32.

Which K-factor does FIDE use?

K = 40 for new players until 30 games and for juniors under 2300 until the end of the year of their 18th birthday, K = 20 below 2400, and K = 10 once a published rating has reached 2400 and remains at that level. If K × the number of games in the period exceeds 700, K is reduced so that the product does not exceed 700. These rules apply from 1 March 2024.

What are my chances with a 100-point deficit?

The expected score is about 36.0%. It counts draws as half a point, so the strict chance of winning is lower when draws are common.

What happens if I draw against a stronger player?

The lower-rated player gains points because their expected score is below 0.5. At 1500 against 1600 with K = 20, a draw is worth +3 points (+4 with K = 32).

Is this tool really free?

Yes, all tools on Kristools are 100% free and accessible without registration.

Is my data protected?

Yes. All processing is performed directly and securely inside your browser. No personal data is sent to our servers.