Vocabulary Memory Landscape: Spaced Repetition & the Forgetting Curve

Vocabulary Deck

Deck size 30 words

Simulated speed 2.0 days/s

Deck State

Click a pillar to review that word, or use the buttons above.

Day

0.0

Avg retention

100%

Words due

How it works

Each vocabulary word has a memory stability S (in simulated days) and a time t since it was last reviewed. Its recall probability follows the Ebbinghaus exponential forgetting curve:

R(t) = e^(-t / S)
  R = probability you still recall the word
  S = stability — larger S means slower decay

Every word starts at R = 100% the moment it is learned or reviewed, then decays continuously. Reviewing a word resets t = 0 and updates S according to the spacing effect:

if R(t) >= 0.2 at review time:
    S_new = S_old * (1 + (1 - R))   // recalled it — bigger gain the closer
                                     // you were to forgetting
else:
    S_new = max(1, S_old * 0.5)     // forgotten — partial relearning reset

Reviewing too early (R near 100%) barely raises S — there was nothing to relearn.
Reviewing right before forgetting (R around 30–60%) gives the largest stability gain — this is the core mechanism behind spaced-repetition apps like Anki, Duolingo and SuperMemo.
Waiting too long (R below 20%) means the word is forgotten and must be relearned, costing progress instead of building it.
Pillar height and colour both encode current retention R(t): tall green = fresh, short red = forgotten.

Real-world relevance: this is a simplified version of the SM-2 / FSRS scheduling algorithms that decide when a language-learning app shows you a word next.

Fresh (high retention) Forgotten (due for review)

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