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Elo Rating Change

ΔR = K (score − expected). Free online Elo Rating Change. Calculate elo rating change online — fast, accurate, mobile-friendly, no signup needed.

ΔR
20.48208
New rating
1,520.48208

Derivation

  1. ├── 01Givenr1 = 1500, r2 = 1600, score = 1, K = 32
  2. ├── 02FormulaΔR: e.K × (n-1 / (1+(10)^((a-t) / 400)))
  3. ├── 03Substitutee.32 × (n-1 / (1+(10)^((a-t) / 400)))
  4. ├── 04Compute ΔR20.48208
  5. ├── 05FormulaNew rating: t+e.K × (n-1 / (1+(10)^((a-t) / 400)))
  6. ├── 06Substitutet+e.32 × (n-1 / (1+(10)^((a-t) / 400)))
  7. └── 07Compute New rating1,520.48208
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§01What is

Understanding the Elo Rating Change

The Elo Rating Change computes ΔR from 4 inputs: your rating, opponent, result (1/0.5/0), k-factor. ΔR = K (score − expected).

Games and puzzles mix math with pattern-spotting. Whether it’s a lottery combination, a dice probability, or a game-theory decision, the numbers behind the fun are worth running properly. The Elo Rating Change sits in that toolkit — it ΔR = K (score − expected). Enter your numbers above and the result updates instantly; every step of the math is shown in the Derivation panel so you can see exactly how the answer was reached.

§02The Formula

How it’s calculated

ΔR = e.K × (n-1 / (1+(10)^((a-t) / 400))) | New rating = t+e.K × (n-1 / (1+(10)^((a-t) / 400)))

Where

r1
Your rating
r2
Opponent
score
Result (1/0.5/0)
K
K-factor
ΔR
Output value
New rating
Output value
§03Practical Example

Step-by-step walkthrough

Scenario

Apply the formula to a realistic set of inputs: Your rating = 1500, Opponent = 1600, Result (1/0.5/0) = 1, K-factor = 32.

  1. 01Start by noting the input — Your rating: 1500.
  2. 02Start by noting the input — Opponent: 1600.
  3. 03Start by noting the input — Result (1/0.5/0): 1.
  4. 04Start by noting the input — K-factor: 32.
  5. 05Substitute these values into the formula: ΔR = e.K × (n-1 / (1+(10)^((a-t) / 400))) | New rating = t+e.K × (n-1 / (1+(10)^((a-t) / 400)))
  6. 06Compute ΔR: the calculator returns 20.4821.
  7. 07Compute New rating: the calculator returns 1520.48.
  8. 08Cross-check the answer by opening the Derivation panel above — every line of math is shown so you can follow the computation end-to-end.
§04Variants

Common Elo Rating Change Problems

The formula gets rearranged depending on which variable you need. Here are the patterns you’ll run into in the real world — find the one that matches your problem and follow the worked steps.

01 · PATTERN

Your rating halved

r1 = 750 (from 1500)

Keep every other input at its default and halve the your rating. See how δr responds.

  1. 01New Your rating: 750
  2. 02Baseline ΔR: 20.4821
  3. 03New ΔR: 31.7618
  4. 04ΔR increases by 55.1% → use this sensitivity to plan for real-world variation.
02 · PATTERN

Your rating doubled

r1 = 3000 (from 1500)

Keep every other input at its default and double the your rating. See how δr responds.

  1. 01New Your rating: 3000
  2. 02Baseline ΔR: 20.4821
  3. 03New ΔR: 0.0101161
  4. 04ΔR decreases by 100% → use this sensitivity to plan for real-world variation.
03 · PATTERN

Opponent halved

r2 = 800 (from 1600)

Keep every other input at its default and halve the opponent. See how δr responds.

  1. 01New Opponent: 800
  2. 02Baseline ΔR: 20.4821
  3. 03New ΔR: 0.559107
  4. 04ΔR decreases by 97.3% → use this sensitivity to plan for real-world variation.
04 · PATTERN

Opponent doubled

r2 = 3200 (from 1600)

Keep every other input at its default and double the opponent. See how δr responds.

  1. 01New Opponent: 3200
  2. 02Baseline ΔR: 20.4821
  3. 03New ΔR: 31.9982
  4. 04ΔR increases by 56.2% → use this sensitivity to plan for real-world variation.
§05FAQ

Frequently asked questions

Yes. The calculator implements the standard formula as documented and returns exact floating-point results. No approximations are used unless noted in the formula.
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